Buried dislocation superlattices are obtained by bonding ultra-thin single crystal Si (001) films on Si (001) wafers. The twist of two Si wafers induces a regular square grid of dissociated screw dislocations and the tilt a 1-D array of mixed dislocation. The Burgers vector is a/2 <110> for both types of dislocation. The atomic displacements and deformations of pure screw and edge dislocations are calculated with an isotropic elasticity approximation taking into account the free surface and the thickness of the upper crystal. It is shown by these calculations that the elastic strain field propagates up to the surface, and quantitative arguments are given to choose the network period / film thickness ratio.