A theoretical model for lattice mismatched pseudomorphically grown heterostructure, which is based on continuum elasticity theory is described. Two distinct types of coherently grown structures are considered, namely, those grown on a thick substrate and these grown on a freestanding one. Special cases of structures that are homogeneous or periodic in some directions are considered. The theory can be applied for an arbitrary crystallographic direction of the heterostructure growth. The model has been applied to AlN/GaN nanocolumn and GaAs/InAs heterostructure. Calculation of strain induced shape deformation is shown.