This paper proposes an application of surface elasticity theory in the analysis of the contact problem at nanoscale. The Fourier integral transform method is adopted to derive the fundamental solutions for the contact problem. As a special case, the deformation induced by a tangential triangle distribution force is discussed in detail. The results indicate some interesting characteristics in nano-contact mechanics, which are distinctly different from those in the macro-contact problem. This study is helpful to characterize and measure the mechanical properties of soft materials through nano-indentation.