The aim of this thesis is to study some astrophysical problems in the context of general relativity. Firstly, we investigate the stability of charged anisotropic spheri- cal as well as cylindrical °uid con¯gurations by observing the appearance of crack- ing/overturning within the matter distribution. In case of spherical system, two cases of polytropic relation between density and pressure are taken into account. We employ the perturbations on material variables via polytropic constant as well as polytropic index and construct the corresponding perturbed form of the force distribution func- tion. It is found that the compact object is stable for feasible choice of perturbed polytropic index in the presence of charge. For cylindrically symmetric object, the cracking is explored by applying density perturbations for two models satisfying spe- ci¯c form of Chaplygin equation of state. We conclude that these models experience cracking for larger values of charge. Secondly, we explore exact anisotropic solutions for charged spherical as well as uncharged cylindrical matter distribution through gravitational decoupling approach. In order to ¯nd the solutions, we consider known solution for isotropic °uid and extend it to two types of anisotropic solutions by imposing density as well as pressure constraints. The behavior of physical parameters, energy conditions and stability of the resulting models is also investigated. It is found that only ¯rst solution is physically acceptable as it meets all the energy bounds as well as stability criterion. Finally, we analyze the anisotropic spherical and cylindrical polytropic solutions. For comoving cylindrical system, we formulate the ¯eld equations for three particular forms of gravitational potential and explore exact solutions for di®erent values of the polytropic index. The values of arbitrary constants are determined by taking mass and radius of a well-known compact star (Her X-1). We ¯nd that two of the models are physically reasonable. The spherically symmetric models are constructed for an xii xiii observer moving relative to matter content using two cases of polytropic equation of state under conformally °at condition which aids to ¯nd a speci¯c form of anisotropy parameter. We obtain models numerically and ¯nd that only ¯rst model satis¯es all the energy conditions as well as stability criterion.