Problems of propagation of elastic surface waves in an isotropic semi-space are considered, with two variants of boundary conditions at the surface of semi-space. Investigation is simplified by introducing potential functions, analogous to plane-strain problems. In the case, when on the surface all three components of stresses are given to be zero, the known generalization of Reyleight plane strain problem is obtained. But in the case when on the surface it is given that normal stresses, one of the shear stresses and one of the shear displacements are equal to zero, then a new dispersion equation is obtained. In this case the surface wave, in contrary to the Reyleight waves, is dispersive. Conditions of existence of the surface wave are obtained.