The conventional contact mechanics does not account for surface tension, however which gets important for micro- or nano-sized contacts. In the present paper, the influences of surface tension on the indentations of an elastic half space by a rigid sphere, a cone and a flat-ended cylinder are investigated respectively, and the corresponding singular integral equations are formulated. Due to the complicated structure of the integral kernel, it is difficult to obtain their analytical solutions. By using the Gauss-Chebyshev quadrature formula, the integral equations are solved numerically firstly. Then, for each indenter, the analytical solutions of two limit cases considering only the bulk elasticity or surface tension are presented. It is interesting to find that, through a simple combination of the solutions of two limit cases, the dependence of load on contact radius or indent depth for general case can be given explicitly. The advanced analytical relations agree well with the numerical results by solving the singular integral equations. The results incorporate the contribution of surface tension in contact mechanics, and are helpful to understand contact phenomena at micro- and nano-scale.