GJ436b is a unique member of the transiting extrasolar planet population being one of the smallest and least irradiated and possessing an eccentric orbit. Because of its size, mass and density, GJ436b could plausibly have an atmospheric metallicity similar to Neptune (20-60 times solar abundances), which makes it an ideal target to study the effects of atmospheric metallicity on dynamics and radiative transfer in an extrasolar planetary atmosphere. We present three-dimensional atmospheric circulation models that include realistic non-gray radiative transfer for 1, 3, 10, 30, and 50 times solar atmospheric metallicity cases of GJ436b. Low metallicity models (1 and 3 times solar) show little day/night temperature variation and strong high-latitude jets. In contrast, higher metallicity models (30 and 50 times solar) exhibit day/night temperature variations and a strong equatorial jet. Spectra and light curves produced from these simulations show strong orbital phase dependencies in the 50 times solar case and negligible variations with orbital phase in the 1 times solar case. Comparisons between the predicted planet/star flux ratio from these models and current secondary eclipse measurements support a high metallicity atmosphere (30-50 times solar abundances) with disequilibrium carbon chemistry at play for GJ436b. Regardless of the actual atmospheric composition of GJ436b, our models serve to illuminate how metallicity influences the atmospheric circulation for a broad range of warm extrasolar planets.