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We present a full wave solver for coupled microstrip lines and multiple vias on printed circuit boards. The formulation is broken down into the interior problem and the exterior problem. The interior problem solves the scattering from a large number of vias inside a parallel plate waveguide, using cylindrical expansion of the magnetic field Green's function. The multiple interactions among vias are evaluated using the Foldy-Lax scattering formula and the solution is accelerated by the sparse matrix canonical grid (SMCG) method. The exterior problem includes coupled microstrip lines with traces passing over anti-pads and is solved using the method of moments (MoM), where RWG basis functions are applied.