Abstract: Based on the successful developments of reduced element for initial value problems (IVPs) and boundary value problems (BVPs), a space-time reduced element is further proposed by taking the elastic string vibration problem (wave equation) as a model problem, and subsequently constructs the corresponding adaptive analysis algorithm. The space-time reduced element inherits all advantages of the reduced elements in IVPs and BVPs and can provide solutions from the reduced element that satisfy the error tolerances in the maximum norm. This paper gives a brief and general introduction to the research progress and presents several typical examples, including forced vibrations and moving load problems, to demonstrate the feasibility, effectiveness and reliability of this method.