We propose a simple model of strained epitaxy with identical atoms being deposited on a substrate which is a disordered alloy. The model is aimed to be suitable for studies of experimentally observed complicated kinetics in such systems with the use of the Monte Carlo technique. Therefore, major attention is paid to the computational efficiency of the model. The techniques developed can be applied to one-dimensional (1D) as well as to two-dimensional heteroepitaxial systems with rectangular lattices of deposition sites. But for simplicity the formalism is presented mainly for 1D systems. In this case the model can be exactly solved at equilibrium with the use of the technique borrowed from the theory of protein folding. This is because in 1D the model of strained heteroepitaxy is equivalent to the Muñoz–Eaton model of protein folding. It is argued that at low temperature the model exhibits slow kinetics characteristic of glassy systems. The existence of the exact solution can be helpful in studying the approach to equilibrium in this complex system.