The plane strain problem is analyzed in detail for a class of isotropic, compressible, linearly elastic materials with a strain energy density function that depends on both the strain tensor ε and its spatial gradient ∇ε. The appropriate Airy stress-functions and doublestress-functions are identified and the corresponding boundary value problem is formulated. The problem of an annulus loaded by an internal and an external pressure is solved. Introduction Theories with intrinsic-or

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... h-scales find applications in the modeling of sizedependent phenomena. In elasticity, length scales enter the constitutive equations through the elastic strain energy function, which in this case depends not only on the strain tensor but also on gradients of the rotation and strain tensors; in such cases we refer to "gradient elasticity" theories. A first attempt to incorporate length scale effects in elasticity was made by Mindlin [34], Koiter [27, 28] and Toupin [42] . They solved also a number of problems and demonstrated the effects of the material length scales that enter the strain-gradient elasticity theories (Mindlin and Tiersten [37], Mindlin [34, 35] , Koiter [28]). Several theoretical issues related to strain-gradient elasticity were addressed later by Germain [23] [24] [25] . More recently,