A technique is presented for calculating the aberrations induced by misalignment of elements of an imaging system with a segmented primary mirror. The misalignment-induced aberration function, derived in terms of a set of five vectors representing small displacements from the aligned position of each element, represents changes in optical path along each ray for the displacement under consideration. This aberration function can be used to conduct parametric tolerance studies of such segmented systems. The behavior of the optical system can be analyzed for variable location of the image plane and at selected points within it. These studies are difficult to conduct with conventional ray trace programs since they involve extensive data processing and great attention to proper se-lection of coordinate systems and transformations. We present results to illustrate the precision levels that should be met in the alignment and metrology of imaging systems with segmented primary mirrors to be operated at visible wavelengths. These precision levels are challenging but achievable with state-of-the-art technology.