A quadrilateral and a triangular element based on the strain approach are developed for static, free vibration and buckling analyses of Reissner–Mindlin plates. The four-node triangular element SBTP4 has the three essential external degrees of freedom at each of the three corner nodes and at a mid-side node; whereas the quadrilateral element SBQP has the same degrees of freedom at each of the four corner nodes. Both elements use the same assumed strain functions which are in the linear variation where bending and transverse shear strains are independent and satisfy the compatibility equations. The use of the strain approach allows obtaining elements with higher-order terms for the displacements field. The formulated elements have been proposed to improve the strain-based rectangular plate element SBRP previously published. Several numerical examples demonstrate that the present elements are free of shear locking and provide high-accuracy results compared to the available published numerical and analytical solutions.