A model is proposed to predict acoustic waves generated in a transversely isotropic cylinder by a laser line pulse extended in beamwidth and time duration, and an application to elastic constants measurement is presented. Documented good agreements are observed in the comparison of experimental and theoretical normal displacements for aluminum cylinders under either ablation or thermoelastic generation. Bulk waves are identified and processed for the elastic constants measurement. The effects of source beamwidth and time duration on wave forms and on the elastic constants measurement are predicted by numerical simulations. For nondestructive evaluation applications using bulk waves, a radius of 0.3 mm appears as a minimum limit for the sample size using a laser source of 0.1 mm beamwidth and 20 ns time duration. Elastic constants of aluminum rods are experimentally measured with very good accuracy.