This paper deals with radial vibrations of dissipative poroelastic spherical shell embedded on the elastic foundation. The case of dissipation results in a transcendental, complex valued frequency equation, and the numerical results are not possible. Hence, the limiting case is considered. When the argument is small, the asymptotic expansions of Bessel functions can be employed and consequently frequency equation can be separated into two real valued equations which in turn give phase velocity and attenuation. In this case, a thick walled hollow spherical shell becomes a thin spherical shell. Phase velocity is computed as a function of the wavenumber, and attenuation is computed against the ratio of outer and inner radii. The results with the elastic foundation are compared with that of without elastic foundation. In the absence of dissipation, the phase velocity is computed and the comparison is made between the present work and earlier works.