Early signs of mechanical characteristic changes are essential for structural health monitoring (SHM). Due to the complexity of civil, mechanical or aeronautical structures, SHM is often faced with high dimensional mechanical characteristics together with limited sensor instrumentation. In this paper, Lasso regression is applied to address this complexity issue, based on its ability for solving large regression problems. The mechanical vibration model is first appropriately transformed into a linear regression model, with its parameters corresponding to small changes in the monitored mechanical characteristics, then these parameters are estimated from mechanical sensor signals under the assumption that most of the parameters are zeros. The performance of the proposed method is illustrated with a simulated truss structure.