Waveguides play one of the key figures in today’s electronics and optics for signal transmission. Corresponding simulations of electromagnetic wave transportation along these waveguides are accomplished by discretization methods such as the Finite Integration Technique (FIT) or the Finite Element Method (FEM). For longitudinally homogeneous and transversely unbounded waveguides these simulations can be approximated by closed boundaries. However, this distorts the original physical model and unnecessarily increases the size of the computational domain size. In this article we present a boundary condition for transversely open waveguides based on the Kirchhoff integral which has been implemented within the framework of FIT. The presented solution is compared with selected conventional methods in terms of computational effort and memory consumption