This chapter presents the application of the Boundary Element Method to the solution of shell governing equations given by first-order shear theory for isotropic materials. The BEM formulation employed is based on the coupling of the Reissner plate boundary integral formulation and the plane elasticity formulation, which are coupled by domain integrals related to curvatures and displacements. The formulation uses fundamental thick-plate and plane stress solutions, allowing for a more straightforward application of the boundary element method. The Dual Reciprocity Boundary Element is used to transform domain-to-boundary integrals.