We present a boundary element model for calculating the mechanical displacements and surface charge distribution for SAW IDTs assuming perfect flat conductors with null mass. For this, we take into account the full 3D piezoelectric surface Green's dyad and solve the integral equation for the electric surface charge when a potential over the metallized area is known using a hybrid elements model. We then observe preliminary results for the charge distribution using the actual G44 component and give a simple formulation for the mechanical displacements.