A detailed analysis of the focusing and collimation of x rays by circular-pore microchannel plates (MCP's), or arrays of cylindrical capillaries, is presented. The focusing effect derives from external reflection of grazing-incidence rays at the interior surfaces of the hollow channels of the MCP and is similar to optical focusingby a spherical mirror. We give the point spread function of an MCP, taking into account surface roughness and misaligned channels. The calculation is based on multiply reflected rays and skew rays and is valid for a spherically curved MCP of any thickness. For comparison with experimental results the effects of a finite source and a detector aperture are also evaluated. This theory is compared with experiment.