A two-dimensional continuum model with couple stress is established for a gridwork which consists of orthogonally intersecting beams rigidly connected at the joints. Equations of motion, boundary conditions, and the constitutive equations are derived, which can be employed to analyze the dynamic as well as static responses of the gridwork. Transverse vibrations and wave propagation are, in particular, investigated by the continuum theory. For the sake of comparison, the finite-element method is employed to calculate the frequencies for several specific gridworks. It is found that the results obtained from the continuum theory agree very well with the finite-element solutions, particularly in the range of long wavelengths.