Masonry bridges are composed of a finite number of distinct interacting blocks that have a length scale relatively comparable to the structure of interest. Therefore, they are ideal candidates for modeling as discrete systems instead of modeling as continuum systems. The discrete finite element method (DFEM) developed by the author to model discontinuum media consisting of blocks of arbitrary shapes is adopted in the static and dynamic analyses of masonry bridges. The developed DFEM is based on the principles of the FEM that incorporate contact elements. DFEM considers blocks as subdomains and represents them by solid elements. Contact elements, which are far superior to joint or interface elements, are used to model the block interactions, such as sliding or separation. In this study, the DFEM is briefly reviewed. Through some typical illustrative examples, the applicability of the DFEM to analysis of masonry arch bridges is examined and discussed. It is shown that the DFEM has the potential to become a useful tool for researchers and practicing engineers in designing, analyzing, and studying behavior of masonry bridges under static and dynamic loading.