Abstract: Based on the established rigorous theory for two dimensional periodic (2DP) medium, a great amount of numerical results for dielectric waveguide array (DWA) with piecewise uniform dielectric constant distribution were presented. Transversal propagation in DWA was analyzed in detail in this paper. Firstly, when the longitudinal wave vector ( k z ) is given. Brillouin dispersion relations between transversal wave vectors were analyzed in various frequencies, and the interactions between space harmonics were also studied. Secondly, when the operation frequency is given, the dispersion relation between transverse wave vectors were analyzed with various longitudinal wave vector or modulation coefficients. Because of interactions between space harmonics getting stronger significantly with k z or modulation coefficients increasing, stop bands can be distinctly viewed and thus transveral propagation in DWA could be comprehensively analyzed.