A numerical model of a tandem reciprocating hydraulic rod seal, consisting of two elastomeric U cup seals, has been constructed. It is applicable to cases in which the stroke length is significantly larger than the seal width. The model consists of coupled steady state fluid mechanics, deformation mechanics, and contact mechanics analyses, with an iterative computational procedure. The behaviors of the two seals are coupled through the pressure∕density in the interseal region and through flow continuity. Results for a typical tandem seal are compared to those of a single seal and a double lip seal.