A viable mechanism for coronal heating is conversion of magnetic field energy into heat through magnetic reconnection in current sheets. Two processes capable of generating current sheets in the solar corona are studied here. The corkscrew kink instability of an axisymmetric magnetic flux tube, as a result of uniform twisting, is addressed first. Linear growth rates of the instability due to a helical perturbation are calculated for a variety of tubes. It is shown that plasma pressure and tube radius reduction are stabilising. The helically symmetric geometry allows us to use an effectively two-dimensional formulation. A magneto-frictional code is developed to simulate relaxation to a second helical equilibrium of the tubes. Lower energy equilibria resulting from the kink are studied. Only one tube, whose twist decays with radius, is shown to result in a true field singularity or a current sheet. The Gold-Hoyle tube relaxes to a smooth kinked equilibrium. Tubes having reversal of a field component result in current concentrations as they kink and relax to a neighboring equilibrium. Plasma pressure reduces the strength of the kink in all cases. The second process resulting in current sheet formation is the interaction of multiple flux tubes. The same frictional code is used to show that repelling tubes move away from each other as the superposed field relaxes to equilibrium. Twisting them together results in current concentrations. Attracting tubes with no neutral point also give rise to current concentrations when they are twisted together and relax to equilibrium. Current sheets are formed when attracting flux tubes, whose initial combined field have a neutral point, coalesce in the absence of plasma pressure. Introducing plasma pressure prevents current sheet formation when the tubes are not twisted together. In case the tubes are twisted together we again see current sheets, the lack of symmetry permitting plasma to flow out from between approaching flux surfaces, allowing them to come into contact. Interaction of unequal attracting tubes results in curved current sheets.