Abstract: Conventional finite element procedures with equal order interpolations for dynamic u-p formulation of saturated soils have been experiencing numerical difficulties for the problems concerning with small permeability and neglectable compressibility of pore-fluid. This paper discusses the stabilization techniques based on the staggered implicit-implicit algorithm and direct α -method to overcome the above mentioned difficulties. Attentions will be paid to the steady state formulations resulted from both approaches. Based on the steady state formulations, the paper will then discuss the determination of the local stabilization parameters, with which a significant improvement for the obtained solutions of pore-pressure can be achieved. Finally, two numerical examples regarding saturated soils subject to a surface cyclic loading are presented to illustrate the effectiveness of the proposed techniques.