A new phenomenological strain gradient theory for crystalline solid is proposed. It fits within the framework of general couple stress theory and involves a single material length scale l cs . In the present theory three rotational degrees of freedom Ο i are introduced, which denote part of the material angular displacement ΞΈ i and are induced accompanying the plastic deformation. Ο i has no direct dependence upon u i while ΞΈ = (1/2) curl u. The strain energy density w is assumed to consist of two parts: one is a function of the strain tensor Ξ΅ ij and the curvature tensor Ο ij , where Ο ij β‘ Ο i,j ; the other is a function of the relative rotation tensor Ξ± ij . Ξ± ij = e ij k (Ο kΞΈ k ) plays the role of elastic rotation tensor. The anti-symmetric part of Cauchy stress Ο ij is only the function of Ξ± ij and Ξ± ij has no effect on the symmetric part of Cauchy stress Ο ij and the couple stress m ij . A minimum potential principle is developed for the strain gradient deformation theory. In the limit of vanishing l cs , it reduces to the conventional counterparts: J 2 deformation theory. Equilibrium equations, constitutive relations and boundary conditions are given in detail. For simplicity, the elastic relation between the anti-symmetric part of Cauchy stress Ο ij , and Ξ± ij is established and only one elastic constant exists between the two tensors. Combining the same hardening law as that used in previously by other groups, the present theory is used to investigate two typical examples, i.e., thin metallic wire torsion and ultra-thin metallic beam bend, the analytical results agree well with the experiment results. While considering the stretching gradient, a new hardening law is presented and used to analyze the two typical problems. The flow theory version of the present theory is also given. ο 2001 Γditions scientifiques et mΓ©dicales Elsevier SAS strain gradient / crystalline solids / couple stress / hardening law * Correspondence and reprints.