The complexity involved in the dynamic response of plates brings many challenges from a mathematical standpoint. In this work, the transient dynamic analysis of elastic shallow shells under uniformly distributed pressure loads, using a dual reciprocity boundary element formulation, is presented. A boundary element formulation based on a direct time-domain formulation using elastostatic fundamental solutions was used. Effects of shear deformation and rotatory inertia were included in the formulation. Shallow shells are modeled coupling boundary element formulation of shear deformable plate and two-dimensional plane stress elasticity. Domain integrals related to inertial terms were treated using the Dual Reciprocity Boundary Element Method. Numerical examples are presented to demonstrate the efficiency and accuracy of the proposed formulation. © 2015 Elsevier Ltd.