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In this paper,a size-dependent shear deformable beam model is proposed within the framework of the nonlocal strain gradient theory.The present model contains the nonlocal effects of the strain field and first gradient strain field as well as high-order shear deformation effect.Two kinds of scale parameters,namely,the nonlocal parameter and the gradient coefficient are introduced to account for the size effect of mechanical properties of nanostructures.Hamiltons principle is applied to derive the governing equations boundary conditions.It can be of interest that the newly developed model reduced to nonlocal continuum theory model by setting material characteristic parameter to zero,and reduced to the strain gradient theory model by setting nonlocal parameter to zero.The analytical solutions of deflection,natural frequencies and critical buckling load are obtained by using the Separation variable method for bending,vibration and buckling analysis respectively.It is found that the natural frequencies and critical buckling load can be increased by increasing the material characteristic parameter or decreasing the nonlocal parameter.And the deflection is the opposite.