The vortex effects of high temperature superconducting (HTS) microstrip resonators have been studied using the theoretical approach developed by Coffey and Clem (CC). A rectangular HTS strip resonator printed on sapphire substrate and subjected to a static magnetic field is considered, where the HTS strip is in the mixed state. An impedance type Green's function is derived which connects the strip current to the electric field around the resonator, in the Fourier transformed domain. Galerkin's procedure is used in the spectral domain to determine the resonant frequency and the unloaded Q value, both of which are computed for different applied fields, reduced temperatures and superconducting strip thicknesses. The results reveal considerable influence of applied field on resonant frequency and quality factor due to vortex motion, which should be considered when designing resonators which operate under external magnetic field.