Abstract: A new 3-node triangular shell element formulation is presented. An advanced co-rotational approach is employed in evaluating the local nodal variables from the global ones to exclude the element rigid-body rotation, thus, to simplify the local element formulation. Different from other existing co-rotational element formulations, additive vectorial rotational variables are employed in the present element formulation, the element tangent stiffness matrix can be obtained by calculating the second derivatives of the energy functional with respect to nodal variables, and all nodal variables are commutative in calculating the differentiation, leading to symmetric tangent stiffness matrices in both the local and global coordinate systems. To overcome locking problems, the line integration approach proposed by MacNeal is utilized to evaluate respectively the assumed membrane strains from three edge membrane strains and assumed shear strains from three edge transverse shear strains. Finally, several shell problems undergoing large displacement and large rotation are solved to demonstrate the reliability, computational accuracy and efficiency of the present element formulation.