A class of solutions describing the interior of a static spherically symmetric compact anisotropic star is reported. The analytic solution has been obtained by utilizing the Finch and Skea (Class. Quant. Grav. 6 (1989) 467) ansatz for the metric potential grr which has a clear geometric interpretation for the associated background spacetime. Based on physical grounds appropriate bounds on the model parameters have been obtained and it has been shown that the model admits an equation of state (EOS) which is quadratic in nature.

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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A new class of exact solutions of Einstein's field equations representing anisotropic distribution of matter on pseudo-spheroidal spacetime is obtained.The parameters appearing in the model are restricted through physical requirements of the model. It is found that the models given in the present work is compatible with observational data of a wide variety of compact objects like 4U 1820-30, PSR J1903+327, 4U 1608-52, Vela X-1, PSR J1614-2230, SMC X-4, Cen X-3. A particular model of pulsar PSR J1614-2230 is studied in detail and found that it satisfies all physical requirements needed for physically acceptable model.

Present paper proposed a new singularity free model of anisotropic compact star. The Einstein field equations are solved in closed form by utilizing Matese & Whitman mass function. The model parameters ρ, p r and p t all are well behaved inside the stellar interior and our model satisfies all the required conditions to be physically acceptable. The model given in the present work is compatible with observational data of compact objects like SAX J 1808.4-3658 (SS1), SAX J 1808.4-3658 (SS2) and 4U 1820-30. A particular model of 4U 1820-30 is studied in detail and found that it satisfies all the condition needed for physically acceptable model. The present work is the generalization of Sharma and Ratanpal (Int. J. Mod. Phys. D 22:1350074, 2013) model for compact stars admitting quadratic equation of state.