The success of the spectral element method with the shallow water equations has prompted us to develop a primitive equation version of the model (SEAM, for Spectral Element Atmospheric Model). We have recently completed this work, making extensive use of the Held-Suarez test cases [Held and Suarez, Bull. Amer. Met. Soc. 1994] to validate SEAM and compare SEAM with other GCM dynamical cores. The results are practically identical to Held-Suarez results from their spherical harmonic spectral model. SEAM also performs well. Results at T42/L20 resolution on 64 nodes of the Cray T3D show that SEAM runs about 9 times faster then the dynamical core from NCAR's CCM3. (At present, SEAM uses an explicit time step 8 times smaller than CCM3, so most of this gain is lost.)