In this work the Monte Carlo method with an empirical potential model for atomic interactions is applied to study reconstruction and intermixing at a Ge-covered Si(001) surface. We investigate the structure and energetics of the 2xn reconstruction which serves as a strain-relief mechanism. The optimal value of n is found to be strongly dependent on the thickness of the Ge overlayer. Si-Ge intermixing is studied using a direct simulation method which includes entropic effects. Ge occupation probabilities in subsurface layers are evaluated as a function of Ge coverage at different temperatures. The results show that strain-relief driven intermixing has a pronounced effect on the surface reconstruction once the Ge coverage reaches a full layer. We also evaluate the effect of temperature on the distribution of Ge in subsurface layers and discuss effects due to kinetic limitations. In agreement with experiments, the study provides a description of the interplay between reconstruction and intermixing at Ge-covered Si(001).