A core-envelope model for superdense matter distribution with the feature — core consisting of isotropic fluid distribution and envelope with anisotropic fluid distribution — is studied on the background of pseudo-spheroidal spacetime. In the case of superdense stars core-envelope models, with isotropic pressure in the core and anisotropic pressure in the envelope, may not be unphysical. Physical plausibility of the models have been examined analytically and using numerical methods.

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We present a new class of solutions to the Einstein's field equations corresponding to a static spherically symmetric anisotropic system by generalizing the ansatz of Finch and Skea [Class. Quantum Grav. 6 (1989) Based on physical requirements, regularity conditions and stability, we prescribe bounds on the model parameters. By systematically fixing values of the model parameters within the prescribed bound, we demonstrate that our model is compatible with the observed masses and radii of a wide variety of compact stars like

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