The behavior of a curved slab bridge decks with uniform thickness under moving load is investigated in this study. Three radii of curvature "R" are used (25, 50 and 75m) along with the straight bridge, R = ∞. The decks are simply supported or clamped along the radial edges and free at the circular edges. The AASHTO[1] standard axle load of the truck H20-44 is used and assumed to move in three track positions on the bridge. The finite element method is employed for the analysis and the ANSYS 5.4 computer program is used for modelling and solving the cases studied. Six different velocities (with a time required to pass the bridge ranging from 0.4 to 2.4 of the natural period of the bridge) are used to investigate the velocity effect of the selected truck on the behavior of the bridge. All the results obtained (stresses and vertical displacements) at mid-span are normalized to the corresponding results of the static load. Results show that the maximum effect reached when the load crossing the bridge in a time (66% to 80%) of the natural period of the bridge. The increase in central displacement due to a combined effect of curvature and velocity is up to 1.75 times the static displacement, while a higher increase obtained for shear stresses.