This paper presents a technique for detecting and locating leaks in a single viscoelastic pipe, by means of transient analysis. The system studied is a reservoir-pipe-valve structure. The viscoelastic behavior of the pipe wall material is modeled by a generalized KelvinVoigt model. To determine the leak location, the mathematical formulation has been solved by the method of characteristics. The approach by the method of characteristics is often chosen because it is based on the concept of acoustic wave propagation which is the main mechanism of all transient events considered. The presence of the two leaks in a pipe partially reflects pressure waves initiated by the sudden closure of a downstream shut-off valve. These waves affect the shape and the amplitude of the time-history-pressure. The computed results describe the influence of the presence of two leaks on pressure time-history and the effect of leaks locations and sizes on the pressure signal behavior. The effect of the pipe wall viscoelasticity on the two leaks detection and sizing is also discussed. The leaks discharges are determined by resolving two independent equations derived from literatures and based on transient analysis. The friction and leaks depths effects on two leaks locations and sizing are involved. (C) 2013 Elsevier Ltd. All rights reserved.