Path integration is presented as an alternative method of solving multiple scattering problems in integrated optics. The method is first derived from coupled-wave theory by using thin-section decomposition and the properties of transmission matrices. A number of applications of the method are then discussed; these include both codirectional and contradirectional devices, devices in which more than two beams are coupled together, and devices operating asynchronously. It is shown that solutions are generated in the form of infinite series, which correspond in all cases discussed to the known analytic solutions.