In this work the lattice deformation of arbitrarily oriented high-T-c superconductor heterostructures of orthorhombic symmetry are calculated within the framework of elasticity theory by using the appropriate boundary condition at the heterointerfaces. We consider the case of very thin films grown coherently on thick substrate crystals and that of freestanding superlattices with coherent heterointerfaces. As an example, the lattice deformation of thin YBa2Cu3O7-delta films grown on SrTiO3 substrates and of freestanding YBa2Cu3O7-delta/PrBa2Cu3O7-delta’ and YBa2Cu3O4/La1.85Sr0.15CuO4 superconductor superlattices is investigated. We determine the symmetry of the distorted unit cell and the strain fields as a function of the orientation of the surface on which the epitaxial growth is performed. In the case of a freestanding superlattice, i.e. in lattice-relaxed conditions, the dependence of the strain tensor components on the thickness of the constituent layers is discussed in detail. Our theoretical model and the relations derived in this work can be applied to a large variety of material systems, in particular to all strained material systems with orthorhombic and higher crystallographic symmetry, i.e. materials of tetragonal crystal structure of classes 4mm, (4) over bar 2m, 422 and 4/mmm, and for all the classes of the cubic crystal structure.