We present a wide grid of models for the structure and transmission properties of warm absorbers in active galactic nuclei (AGN). Contrary to commonly used constant density models, our absorbing cloud is assumed to be under constant total (gas plus radiation) pressure. This assumption implies the coexistence of material at different temperatures and ionization states, which is a natural consequence of pressure and thermal equilibrium. Our photoionization code allows us to compute the profiles of the density, the temperature, the gas pressure, the radiation pressure and the ionization state across the cloud, and to calculate the radiative transfer of continuum and lines including Compton scattering. Therefore, equivalent widths of both saturated and unsaturated lines are properly modeled. For each pair of the incident spectrum slope and the ionization parameter at the cloud surface there is a natural upper limit to the total column densities of the cloud due to thermal instabilities. These maximum values are comparable to the observational constraints on the column density of warm absorbers which may give support to constant total pressure models. In all models we note considerable absorption around 6.4 keV which modifies the intrinsic relativistically broadened iron line profile originating in an accretion disk illuminated atmosphere. Our models can be applied to fitting the spectroscopic data from the XMM-Newton and Chandra satellites.