This study considers the propagation of Rayleigh waves on the stress‐free surface of a viscoelastic, porous solid saturated with viscous fluid. The surface pores have the option of being either sealed or fully opened. The dispersion equation is obtained in the form of a complex irrational expression due to the presence of radicals. After rationalizing to an algebraic form, the dispersion equation is solved numerically, for exact complex roots. These roots are resolved for velocity and attenuation of the inhomogeneous propagation of Rayleigh waves in the poro‐viscoelastic solid half‐space. Effects of frame anelasticity, pore‐fluid viscosity, frequency, and pore characteristics are observed numerically on the velocities of existing Rayleigh waves. Behavior of the elliptical particle motion for these waves is studied inside and at the surface of the porous solid. With the sealing of surface pores, these waves should be more sensitive to the changes in porosity and tortuosity. An exclusive contribution of dissipation due to the anelastic frame and/or the viscous pore‐fluid is the existence of an additional inhomogeneous wave that satisfies the radiation condition for surface waves. This additional surface wave is more likely when surface pores of the dissipative porous medium are sealed.