Neural field models, in which populations of neurons are described through ensemble-averaged properties such as firing rate and axonal flux, have been well-used to describe electroencephalogram (EEG) effects in natural sleep, anaesthesia and epilepsy. Changes in EEG due to stimulation by electromagnetic fields have also been studied. However, experimental data concerning transcranial magnetic stimulation (TMS) is dominated by measurements of motor-evoked potentials (MEPs). To use neural fields for TMS, a model of the MEP is required. In this work, an existing model has been augmented by addition of populations of cells describing stages of the MEP pathway previously neglected by neural field models. The model includes coupled populations of excitatory and inhibitory layer 2/3 cortical neurons, stimulated by an external field. These populations feed an additional population of layer 5 neurons, which also couples weakly to the external field. The layer 5 neurons feed motoneurons, from which a measure of the motor-evoked potential is constructed. After some tuning of parameters, the extra populations have resulted in a better model of the MEP than previously present in neural field models. The model reproduces the non-linear response to an increase in stimulation amplitude. With a paired-pulse protocol it reproduces the experimental effects of intracortical facilitation and long-interval intracortical inhibition, though it shows only weak short-interval intracortical inhibition. The experimental direct and indirect waves of activation from the layer 5 neurons are not adequately reproduced. Small changes in synaptic weight can give much greater changes in MEP response. In conclusion, the model is promising but it raises questions about whether neural field models are really appropriate for the study of many TMS effects.