Toroidal flow velocities of the order of the local sound speed and poloidal flows exceeding theoretical predictions have been observed in several tokamaks. Steady toroidal and poloidal flow effects are studied using dissipationless single-fluid and two-fluid theory, with electron inertia neglected in the latter case. An exact analytic treatment of the two-fluid system, with the electron and ion temperatures both assumed to be flux functions and ion poloidal flows neglected, reveals a much wider class of rotation profiles than those corresponding to rigid body rotation of flux surfaces, which is required by ideal magnetohydrodynamics MHD. A generalized expression is obtained for the variation of the density on a flux surface in the presence of flows, and a relation is established between the rotation and temperature profiles that makes it possible to test experimentally the assumption of rigid body rotation. Relaxing the assumption that ion temperature is a flux function leads to a still wider class of possible profiles. It is shown that ion momentum balance in the absence of ion poloidal flows implies a Grad-Shafranov equation that is structurally similar to the standard ideal MHD form of this equation. Leading order ion poloidal flow corrections to the Grad-Shafranov equation are also computed.