In the paper, a new, efficient, modified three dimensional spectral domain solution is achieved for generalised planar periodic waveguides, in which a ‘modal spectrum’ is set up with respect to periodic loaded stubs. Slow-wave propagation characteristics on structures such as finlines and slotlines are investigated. Important behaviour, such as passband and stopband, related to cutoff and resonant frequencies is discussed in detail. The computed results are found to have good agreement with the measured ones.