Numerical analyses are presented for the laser-generated guided elastic waves in hollow cylinders. The transient waveforms excited by the ablation source (AS) and the evaporation source (ES), due to the ablation and the evaporation of oil induced by impinging laser pulse, are calculated numerically by modeling different time-dependencies, i.e. the former is considered as Heaviside step function and the latter is assumed to be Dirac Delta function. Instead of using classical integral transform, the method of eigen-function expansion is employed, by which time-dependent displacement at the outer surface of hollow cylinders will be expressed by summation of longitudinal and flexural type modes. This formula is particularly suitable for analyses of generation efficiency of each guided elastic mode. And the waveform of total radial displacements were analyzed using a short-time Fourier transform (STFT).