The finite element method was employed to simulate the dynamic stress waves and residual stresses induced by laser impacting the cylindrical surface of round rod made of 2024 aluminum alloy. During simulation, the code ABAQUS/Explicit was firstly utilized to simulate the process of the stress wave propagation in the rod with the diameter 16 mm, which was induced by the laser shock wave with peak value 2 GPa. Subsequently, the other code ABAQUS/Standard was used to calculate further the residual stresses distributed in the cylindrical surface of rod. Based on the simulation results, the effects of the rod diameter on the attenuation of the peak pressure of the stress wave and the residual stress distribution were investigated. Corresponding experiments were carried out to validate the calculated results as well. The results indicate that the peak pressure of the stress wave induced by the 2 GPa shock wave decreases rapidly to 250 MPa within 400 ns in the round rod with diameter 16 mm. After laser shocking, an uneven residual stresses are distributed in central region of the impacted surface, and tensile residual stresses are formed at the center, where the value of residual stresses S11 reaches 42 MPa. While compressive residual stresses are formed in other impacted areas(radius from 0.5 mm to 1.5 mm), where the compressive residual stresses S11 are roughly 250 MPa. During the propagation of the stress wave, the decay rate of its peak pressure decreases with the enlarging rod diameter, and the compressive residual stresses distributed on the cylindrical surface increase with the increasing rod diameter.