A new discrete Monte Carlo technique suitable for simulations of the kinetics of heteroepitaxial crystal growth has been developed and tested on a 103atom system. The technique offers sizable speed advantages over previous simulation methods and allows for realistic three‐dimensional studies of the kinetics of both pseudomorphic and misfit growth modes and of the transformation between them. Elements of the method are of general utility and can also be used to substantially improve the efficiency of continuous‐space Monte Carlo and molecular dynamics simulations of growth and other atomic transformations.