High-Q (quality factor) resonators are a versatile class of components for radio frequency micro-electromechanical systems . Phononic crystals provide a promising method of producing these resonators. In this article, we present a theoretical study of the Q factor of a cavity resonator in a two-dimensional phononic crystal comprised of tungsten rods in a silicon matrix. One can optimize the Q of a phononic crystal resonator by varying the number of inclusions or the cavity harmonic number. We conclude that using higher harmonics marginally increases Q while increasing crystal length via additional inclusions causes Q to increase by orders of magnitude. Incorporating loss into the model shows that the silicon material limit on Q is achievable using a two-dimensional phononic crystal design with a reasonable length. With five layers of inclusions on either side of the cavity, the material limit on Q is achieved, regardless of the harmonic number.