The film bulk acoustic resonator (FBAR) is an emerging piezoelectric device, widely spreading for sensing applications and in many commercial products like cell phones for its high working frequency and small size. This work presents a complete approach for the modeling and design of a ZnO-based Solidly Mounted Resonator (SMR) in 2D and 3D models. The finite element method was used to perform its simulation at the frequency range from 1 to 3 GHz. In addition, in order to suppress or minimize horizontal parasitic modes, the geometry of the electrodes has been optimized by comparing the pentagonal and the rectangular shapes. Finally, the size of the models has been reduced to save computing resources by setting symmetry boundary conditions.