Cylindrical charges are widely used in engineering blasting, yet the three-dimensional propagation mechanism of the associated stress waves remains inadequately understood. This study aims to investigate the effects of key wave source parameters on stress wave propagation and rock damage in cylindrical charge blasting. A semi-analytical solution for spherical stress wave propagation in a full elastic space is developed to theoretically describe the stress field, and a computational model for cylindrical charges is established based on the superposition principle of equivalent spherical charges. Numerical simulations using the RHT constitutive model are then performed to verify the theoretical predictions and further investigate stress wave propagation and rock damage. The results show that the attenuation index of radial stress decreases from 1.5 to 1 as the loading rate increases. Higher loading rates produce more but shorter cracks, whereas lower rates result in fewer but longer cracks. The blast-induced damage region shifts from the detonation direction toward the horizontal plane with increasing detonation velocity, and the resulting rock damage exhibits a conical distribution controlled by the initiation point. These findings provide practical guidance for optimizing cylindrical charge blasting and controlling crack patterns in engineering applications.