In this work, the modal and harmonic analysis of elastic shallow shells, using a Dual Reciprocity Boundary Element formulation, is presented. A boundary element formulation based on a direct time-domain formulation using the elastostatic fundamental solutions was used. Effects of shear deformation and rotatory inertia were included in the formulation. Shallow shell was 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. Several examples are presented to demonstrate the efficiency and accuracy of the proposed formulation. © 2014 Elsevier Ltd.