The simultaneous influence of surface and couple stresses on the nonsymmetrical frictionless indentation of a linearly elastic, homogenous, and isotropic half plane under a tilted, rigid, flat-ended indenter with sharp, square corners was investigated by adopting existing continuum-based models. The half plane was mathematically constituted by the surface layer and bulk materials, and the mechanical response of each component was described by means of the Gurtin-Murdoch surface-elasticity and couple-stress elasticity theories, respectively. Under an applied eccentric load, the geometric compatibility condition for points within the contact region and the equilibrium conditions of the indenter were utilized to establish a set of governing equations for the unknown contact pressure. Selected efficient numerical schemes, based mainly upon the solution discretization, the standard collocation technique, and the fundamental solution of an elastic half plane under surface normal loads, were developed to construct the solution of complete and receding contacts numerically. Obtained results from an extensive numerical study apparently reflect the crucial effects of the surface and couple stresses on the indentation behaviors of the tilted indenters and the elastic response of the bulk material, and, in particular, the strong size-dependency of solutions when the width of the indenter becomes comparable to the length scale parameter of the surface and bulk materials. These characteristics not only provide valuable information for a better understanding of the mechanical properties of materials by micro-/nano-indentation tests, but also facilitate a basis for further investigations in the area of micro-/nano-mechanics.