This paper presents a simple and effective strain smoothing method (the strain-smoothed element method) for 3-node triangular and 4-node tetrahedral solid finite elements. While piecewise constant strain fields are constructed through smoothing domains in previous strain smoothing methods, in the proposed method, linear strain fields are constructed within finite elements using constant strains of neighboring finite elements. When the new strain smoothing method is adopted, the triangular and tetrahedral solid finite elements pass all the basic tests; patch, isotropy and zero energy mode tests, and show improved predictive capability. The formulation of the proposed method is presented in detail. Through various numerical examples, we demonstrate the accuracy improvement achieved. •We propose a new strain smoothing method for triangular and tetrahedral finite elements.•Linear strain fields are constructed within elements without using special smoothing domains.•The proposed strain-smoothed elements pass patch, isotropic and zero energy mode tests.•Its improved performance is demonstrated through various numerical examples.