The problem of determining the shell-side Taylor dispersion coefficient for a shell-and-tube configuration is examined in detail for square and hexagonal arrays of tubes for the case when the shell side flow is laminar and parallel to the tubes. A multipole expansion method is employed to determine fluid velocity and concentration field for the fluid on the shell side. The numerical results for the shell side Taylor dispersion coefficient are compared with those by a cell theory. The cell theory agrees well with the numerical results at small area fractions and gives better estimates for hexagonal arrays. Finally, we present formulas for determining Taylor dispersion coefficient for the periodic arrays.