Abstract: A new four-node triangular element (T4) is proposed, and the area-weighted strain smoothing technique and smoothed FEM are implemented to this element. Two volumetric locking-free schemes are proposed, including the edge-based strain smoothing schemes for T4 element (T4-EAW) and the selective domain-based strain smoothing scheme (T4-pEAW/NAW). The benchmark numerical examples show that those two proposed methods can avoid volumetric locking and pressure oscillation, and the T4-pEAW/NAW model can also improve the accuracy of the displacement calculation by adjusting the Deviator strain energy by parameter p. Compared with the traditional smoothed finite element method using the triangular element, those two proposed methods using the T4 element avoid pressure oscillation.