Abstract In this study 2N algorithm deals with the problems of linear elastic structures and discuss the spurious resonance from the assumption of time integration when natural frequency approach of load frequency. The process of algorithm is analyzed by mathematical model building on algorithmic method which is like high precision direct integration method(HPD) or state space method(SS). At the same time, 2N algorithm is using momentum equilibrium for the minimum of linear error. Because 2N algorithm is algorithmic method, it has not any frequency dissipation. In order to reduce the high frequency effects in the space discretization the frequency of model is first analyzed and Rayleigh damping is chosen later. After this process 2N algorithm can reduce the high frequency effects gradually. Keywords：2N algorithm、HPD、SS、momentum equilibrium、spurious resonance