We combine dissipationless N-body simulations and semi-analytic models of galaxy formation to study the spatial and kinematic distributions of cluster galaxies in a ΛCDM cosmology. We investigate how the star formation rates, colours and morphologies of galaxies vary as a function of distance from the cluster centre and compare our results with the CNOC1 survey of galaxies from 15 X–ray luminous clusters in the redshift range 0.18 < z < 0.55. In our model, gas no longer cools onto galaxies after they fall into the cluster and as a result, their star formation rates decline on timescales of ∼ 1 − 2 Gyr. Galaxies in cluster cores have lower star formation rates and redder colours than galaxies in the outer regions because they were accreted earlier. Our colour and star formation gradients agree with those derived from the data. The difference in velocity dispersions between red and blue galaxies observed in the CNOC1 clusters is also well reproduced by the model. We assume that the morphologies of cluster galaxies are determined solely by their merging histories. A merger between two equal mass galaxies produces a bulge and subsequent cooling of gas results in the formation of a new disk. Morphology gradients in clusters arise naturally, with the fraction of bulge-dominated galaxies highest in cluster cores. The fraction of bulgedominated galaxies inside the virial radius depends on the mass of the cluster, but is independent of redshift for clusters of fixed mass. Galaxy colours and star formation rates do not depend on cluster mass. We compare the distributions of galaxies in our simulations as a function of bulge-to-disk ratio and as a function of projected clustercentric radius to those derived from the CNOC1 sample. We find excellent agreement for bulge-dominated galaxies. The simulated clusters contain too few galaxies of intermediate bulge-to-disk ratio, suggesting that additional processes may influence the morphological evolution of disk-dominated galaxies in clusters. Although the properties of the cluster galaxies in our model agree extremely well with the data, the same is not true of field galaxies. Both the star formation rates and the colours of bright field galaxies appear to evolve much more strongly from redshift 0.2 to 0.4 in the CNOC1 field sample than in our simulations.