This paper studies the influence of the ionospheric conductance on the size of the Earth's magnetopause and bow shock under the following assumptions: ( I) the ionosphere, treated as a spherical shell, has a uniform Pedersen conductance Sigma(p) and a zero Hall conductance, and (2) the Earth's dipole moment is due southward and the interplanetary magnetic field (IMF) has only south component (B-z < 0). The size of the magnetopause and bow shock is characterized by the geocentric distances of their intersection points with the three axes of the GSE frame, i.e., the subsolar point, the dawn-dusk flank point, and the north-south top point. Given the solar wind conditions, and the values of B-z and Sigma(p), a quasi-steady state of the system is obtained by 3-D global MHD simulations. It is shown that the influence of Sigma(p) on the size of the magnetopause and bow shock is significant in the range of about 1 similar to 5 S but negligible otherwise. As Sigma(p) increases, the magnetopause and bow shock expand outward as a whole, and the former expands less than the latter so that the magnetosheath widens. The variation of the flank point position of the magnetopause with Sigma(p) depends on the magnitude of B-z : the flank point shifts inward with increasing Sigma(p) for weak southward IMF cases and outward otherwise. The above-mentioned results indicate that the effect of the ionospheric conductance should be incorporated in constructing empirical models of the magnetopause and bow shock.