In the traditional layered piezoelectric structures, high stress concentrations could cause the structural failure in interlayer surfaces due to repeated strain reversals. To overcome the performance limitations of these structures, the concept of Functionally Graded Materials (FGMs) has been introduced to improve the lifetime, integrity, and reliability of these structures. In this paper, the free and forced vibration of radially polarized Functionally Graded Piezoelectric (FGP) cylinders under different sets of loading are studied. Material properties such as piezoelectric, elastic and permittivity are assumed to change along its thickness, based on a specific gradation function. Four-parameter power law distribution is used to grade the volume fraction of the constituents comprising of PZT-5A and PZT-5H. Material property is assumed to be temperature dependent for a few numerical studies. The present modeling approach is validated by comparing the free and forced vibration of radially polarized Functionally Graded Piezoelectric (FGP) cylinders with those reported in the literature. The effects of material composition, loading and boundary conditions on the dynamic behavior of FGP cylinder are described. Since the modeling of functionally graded piezoelectric systems is challenging, the present study can help in the design and analysis of FGP cylinders.