This paper presents a novel implementation of GPU computing for boundary element method (BEM) formulation of plates. The new GPU code written in CUDA Fortran alters three kernels: the calculation of influence matrices, the solution of equations, and the computation of internal values. Comparisons for computation time and different GPU architecture are presented. The formulation is implemented for both constant and quadratic elements. The efficiency of the parallel quadratic code is demonstrated via analysis of practical building slabs. The benefits of parallel computing of the solution of the system of equations and of points inside the domain are discussed.