<p>The paper presents the results of numerical investigations of natural vibrations of truncated straight conical shells filled with an ideal compressible fluid. The thickness of the shells is non-uniform along the generatrix and varies according to different laws. The behavior of the elastic structure and fluid medium is described within the framework of the classical shell theory and Euler equations. The relations of the shell are reduced to a system of ordinary differential equations with respect to new unknowns. The acoustic wave equation is transformed to a system of differential equations using the method of generalized differential quadrature. The solution of the stated boundary value problem is found by the Godunov orthogonal sweep method and reduced to the calculation of the natural frequencies. For this purpose, the stepwise procedure is used in combination with the procedure of subsequent refinement of the calculated values in the obtained range by the Muller method. The validity of the obtained results is confirmed by comparison with known numerical solutions. For shells with different cone angles, fluid levels and combinations of boundary conditions the dependences of the lowest frequencies obtained at the power-law and harmonic thickness variation have been investigated in detail. The influence of boundary conditions on the existence of configurations, which could provide an increase in the fundamental frequency in comparison with the shells of constant thickness subject to weight restrictions, has been evaluated. The study confirms the existence of differences in maximization of the frequencies between the completely and partially filled shells.</p>