The object of research is the frequency characteristics of a statically determined flat truss on two supports with a complex lattice and rectilinear horizontal chords. It is assumed that the mass of the truss is distributed uniformly over the nodes, and the stiffnesses of the elastic rods are the same. Method. According to the Dunkerley formula, an analytical estimate of the fundamental frequency of its natural oscillations is found. The vibrations of the masses are vertical. The forces in the rods are found by cutting out the knots. The rigidity of the structure is calculated by the Maxwell-Mohr formula. The generalization of a series of particular solutions for trusses with a successively increasing number of panels is carried out by induction using the Maple computer mathematics system. The common terms of the sequence of coefficients are determined from the solution of linear homogeneous recursive equations. To verify the solution, the fundamental frequency is calculated numerically as the first frequency of the spectrum. Results. Comparison of the analytical solution with the numerical one shows that the accuracy of the analytical estimate from below is quite high and increases with the number of panels. Spectral constants and isolines are found in the frequency spectra of a family of regular trusses.