A method for inverting VLF/LF ionosounder data to obtain ionospheric conductivity profiles is described. The method is applied to altitudes below about 70 km, where the propagation can be assumed to be isotropic. Two cases are evaluated: (1) model ionospheres for which artificial data are generated by calculating reflection coefficients and (2) actual ionospheres for which reflection coefficients are measured by VLF/LF ionosounders during a strong solar proton event. Estimates are given of altitude ranges inside which ionosounder data contain information about conductivity and outside which the inversion breaks down. Calculated profiles are shown to agree well with model profiles within those altitude ranges. Profiles calculated for the solar proton event of September 23, 1978, are similar in magnitude and structure to those which occurred during earlier strong solar proton events.