This paper presents a theoretical framework for an analytical investigation of multipath characteristics of frequency diverse arrays (FDAs), a task which is attempted for the first time in the open literature. In particular, transmitted field expressions are formulated for an FDA over a perfectly conducting ground plane first in a general analytical form, and these expressions are later simplified under reasonable assumptions. Developed formulation is then applied to a uniform, linear, continuous-wave operated FDA for the particular case of linear frequency increments, and closed-form solutions are established. Time dependence of the FDA array factor is next eliminated by calculating the average power received by an isotropic antenna at a given observation point. Field and power derivations are repeated for a conventional phased array to establish a performance benchmark. Numerical simulations are conducted for special test cases to demonstrate the advantages of FDAs over conventional phased arrays in terms of multipath propagation.