Fundamental petrographic controls on ignimbrite strength are examined, and those aspects of the texture and fabric of the rocks which are primarily responsible for the strength of ignimbrite identified. The range of strength exhibited by ignimbrite is quantified, and the value of common, non-destructive indices as predictors of ignimbrite strength assessed, with predictive equations presented where appropriate. Models for the strength, jointing, and geomorphic development of an ignimbrite sheet are derived. Compressive, shear, and tensile strengths, measured by using standard techniques, provide the basic geomechanical data; strength indices (density, porosity, rebound hardness, slake durability, and ultrasonic wave velocity) and petrographic measurements (bulk rock chemistry, mineralogy, texture, fabric, and the extent of post-depositional alteration) are compared with these data using regression analysis. Textural and fabric parameters are determined using image analysis, optical microscopy, and scanning electron microscopy to quantify the size, shape, and three-dimensional arrangement of the components making up the ignimbrite. Ignimbrites have highly variable strength, but in all forms of loading are classified as weak rocks. The strength variation ranges over at least two orders of magnitude for the compressive strength, and one order of magnitude for the tensile strength. Such variation may occur within a single vertical section through an ignimbrite sheet. Marked softening upon saturation occurs for all forms of strength, and ignimbrites show considerable plastic deformation prior to failure - rarely is a brittle failure mechanism exhibited. Bulk rock properties and index measurements reflect the low strength values; ignimbrites have low bulk densities, high porosities, low rebound hardnesses, and low velocities of ultrasonic wave transmission. They display a highly variable response to slaking, with some being almost completely broken down by gentle agitation, and others remaining unaffected. The porosity provides the best indicator of compressive strength, and predictive equations relating dry and saturated compressive strength to porosity are presented. Dry bulk density can also be used as a predictor of compressive strength, but the relationship is not as strong as that for porosity. Predictive equations relating the compressive and tensile strength to the Schmidt hammer rebound provide good indicators of major variations in rock strength, but are insensitive to subtle strength changes. Ultrasonic wave velocity is a useful laboratory indicator of the tensile strength of ignimbrite. Unlike those for other index properties, the relationship between ultrasonic wave velocity and tensile strength is insensitive to changes in the moisture content of the rock. This means it should also, with appropriate calibration, be applicable under field conditions. The groundmass fabric exerts the primary control over the compressive and tensile strengths of ignimbrite. The influence of groundmass fabric is modified by the size of the crystals and clasts included within the ignimbrite, but these two components are of less significance than the groundmass fabric. Shear strength is not readily related to petrographic parameters. Compressive strength is controlled by the packing of the groundmass shards (their alignment and the density of pore filling), and the extent to which the shards are welded at their points of contact. These factors control the distribution of stresses in the material, and the ease with which microfractures can propagate through the groundmass. The size of crystals and pumice clasts controls the concentration of stresses around such inhomogeneities, and hence the initiation of microfractures. However, the proportion of such clasts is not important, so long as a sufficient number are present to initiate microfractures. Tensile strength is controlled by the degree of alignment of the shards, and the hardness of the pumice clasts; aligned shards and hard pumice clasts result in an ignimbrite with high tensile strength. Only a small anisotropy exists in terms of the direction of shard alignment with respect to the direction of principal stress. Idealised models of joint development, hillslope form, and geomorphic development are based upon predictable variations in the primary petrographic features recognised as influencing the strength of the ignimbrites - the groundmass fabric and the nature of shard welding. Variations in these properties caused by emplacement conditions result in predictable strength variations, and in characteristic jointing patterns associated with each strength zone. It is these strength and jointing patterns which dictate the means by which erosion can affect an ignimbrite, and hence the resulting landform patterns.