In our previous studies we derived the exact closed structural theories for a set of plane regular and quasi-regular framed structure of girder type using the method of `gluing’. In the paper presented, we extend this approach to problems of small vibrations of plane regular elastic girders of orthogonal structure. The main attention is paid to vibrations of a girder with an elementary cell in the form of a rectangular having two diagonal rods that do not affect to each other. Eliminating some rods out from this structural element, we can obtain a comparatively wide class of regular, quasi-regular, and non-regular girders of orthogonal structure. We realize the general strict statement of the problem of small vibrations of the girder in details for the problems of natural vibrations and forced vibrations. These solutions are illustrated by numerical examples.