A description of the acoustic pressure versus time is obtained for a finite cylindrical source whose initial overpressure is constant and uniform. Small signal analysis is used and the medium is considered dissipationless. The results show a short leading condensation followed immediately by a rarefactive impulse with a long tail which ends in a second rarefactive pulse of smaller amplitude. The analytical results are amenable to numerical methods for obtaining pressure disturbances from cylindrical sources of given lengths and radii.Subject Classifacation: [43]20.55, [43]20.15.