Small free vibrations of a rotating cylindrical shell of the infinite length which is in a contact with rigid cylindrical rollers are considered. The system of the linear differential equations of the shell vibrations is deduced. By means of the expansion of solutions in Fourier series on circumference coordinate the system of the algebraic equations for the approximate definition of the vibration frequencies and the mode shapes is received. It is shown, that for any number $n$ of uniform distributed rollers, the approximate values of the first $n$ vibration frequencies and the mode shapes can be found in explicit form. On the basis of an orthogonal sweep method the algorithm of the numerical solution of a boundary value problem describing rotating shell vibrations is developed. Comparison of analytical and numerical results is performed. The received approximate formulas for frequencies and algorithm for their definition by the numerical method can be used for the designing the centrifugal concentrators inte