Elastic properties of three-dimensional lattices are usually anisotropic. This fact limits the range of applicability of lattice models in solid mechanics problems. In the present paper, we propose a simple three-dimensional lattice model with isotropic elastic properties. A quasi-random lattice is generated by randomly displacing particles of the face-centered cubic lattice. Then particles are connected by linear and angular springs such that initially forces in all springs are equal to zero. It is shown numerically that the resulting quasi-random lattice has isotropic elastic properties, provided that amplitudes of random displacements are sufficiently large. Poisson’s ratio of the lattice depends on number of angular springs per particle and stiffnesses of these springs. In the present model, values of Poisson’s ratio belong to the interval [0;0.41]. The model can be used, in particular, for simulation of deformation and brittle fracture of rocks in hydraulic fracturing.