This paper desfcribes the formulation for the analysis of the free vibration of a circular cylindrical shell with elastic supports by the transfer influence coefficient method. This method was developed on the base of the concept of the successive transmission of dynamic influence coefficients. The analysis algorithm for circular cylindrical shell elastically restrained by springs, which plays an important role in many industrial fields, is discussed. The supporting springs have the axial, circumferential, radial and rotational spring constants uniformly distributed along the circumference of the shell. The simple computational results on a personal computer demonstrate the validity of the present method, that is, the numerical high accuracy, the high speed analysis method and the flexibility for programming, compared with results of the transfer matrixmethod and reference. We also confirmed that the present algorithm could obtain the solutions of high accuracy for system with a number of intermediate rigid supports. And we could easily treat the intermediate support and all boundary conditions by adequately varying the values of spring constants.