An accurate field theory solution for calculating the hybrid eigenmodes of quasiplanar structures is introduced which includes both the influence of the finite strip thickness and waveguide housing grooves. Using the transverse resonance method the size of the characteristic matrix equation is kept constant even for an increasing number of discontinuities. Dispersion characteristics of various structures consisting of at least one isolated strip are presented. The fundamental EH0-modes mainly depend on the finite strip thickness, while increasing waveguide grooves lead to a significant reduction of higher-order-mode cutoff frequencies.