We study elastic oscillations of plane elastic beam of girder type, which is a rod system of a girder type significantly elongated in one direction. This system has an orthogonal structure. Elementary rectangular cells include two diagonal rods which work independently from each other. We develop the approximate dynamical models of composite beam, which can be regarded to be the discrete analogues of Timoshenko and Bernoulli models of the theory of uniform beams. Such models have undoubted advantages since in this case the problem of natural oscillations of composite beams can be reduced to much more simple discrete one-dimensional problems on eigenvalues. Efficiency of the models proposed is illustrated by specific examples.