This paper presents an approach to model transmission and reflection phenomena of elastic guided waves in plates. The formulation is applied to plate structures containing notches, inclined edges, delaminations or (adhesive) joints. For these cases, only the thickness direction of the structure needs to be discretized at several locations, while the direction of propagation is described analytically. Consequently, the number of degrees of freedom is very small. Semi-infinite domains can be modeled, in which case the radiation condition is fulfilled exactly. Traction boundary conditions are introduced on the plate surface without requiring a mesh along the surface. Results are validated against conventional finite element implementations, showing the accuracy of the proposed approach and a reduction of the computational costs by typically 2–3 orders of magnitude.