Here is reported, from the theoretical point of view, how a stressor layer included in a nanomesa can modify the growth process of a mismatched material : critical thickness for 2D-3D transition, and optimal location of nucleating dots by means of the induced stress field. This stress field depends on both design parameters and sign of the misfit between the stressor and the mesa material. This is exemplified by the case of InAs deposition on InP mesas which include an InGaAs stressor. A second case in which stress field plays a key role is the capping of dots on top of nanomesas . We investigate the case of Si capping of a system where one Ge dot covers the top of each mesa of a very dense array of Si nanomesas. Upon several basic assumptions, different capping processes are simulated, in order to predict the more stable one. We point out very different behaviors for pure Si capping or SiGe capping. How long it takes for recovering a flat surface strongly depends on the presence of a thin Ge surface layer.