We studied propagation of the electromagnetic waves in a hybrid planar structures containing uniaxial hyperbolic material. For structures, satisfying to the set of special requirements, our analysis showed existence of surface waves. This result is different from several well-known cases when hybrid stricture contains conventional dielectric instead of hyperbolic material. Using derived dispersion relations, we also conducted comparative analysis of the discovered surface waves with the characteristics of surface plasmons. We evaluated relevance of obtained results to the experimental situation for hybrid structures based on currently available materials.