A theoretical investigation of the characteristics of the tunneling current in the scanning tunneling microscope (STM), taking into account the atomic structure of a nanoprotrusion tip ending in a single atom and nanostructure features of the sample, is presented. The current is determined from the total wave function for the tip-sample system. Scattering theory is used to determine the total wave function in terms of the local Green’s functions. Because of the lateral confinement of the electrons by the mesoscopic size of the probing tip, the current through the STM exhibits a Gaussian spatial dependence. It is shown that the constant current mode of operation does not give an accurate description of the topographical features of the potential and hence the surface of the sample.