In this study, the behavior of vibration of sandwich cylindrical shells covered by functionally graded coatings and resting on the Pasternak elastic foundation considering combined influences of shear stresses and rotary inertia are examined. It is assumed that the effective material properties of functionally graded coatings changes exponentially in thickness direction. The modified Donnell type equations of motion of functionally graded and homogeneous sandwich cylindrical shells on the Pasternak elastic foundation are deduced using the first-order shear deformation theory. Basic equations are reduced to an algebraic equation of the sixth order and numerically solving this algebraic equation gives the dimensionless fundamental frequency. The expressions for the dimensionless fundamental frequencies of functionally graded and ceramic coated sandwich cylindrical shells with and without taking into account the effects of Pasternak elastic foundation and shear stresses obtained in a special case. Calculations, the influences of an elastic foundation, compositional profiles of coatings, shear stresses, rotary inertia, and sandwich shell geometry parameters on the nondimensional fundamental frequency are described. The results are verified by comparing the obtained values with those in the existing literature.