The critical state model has been used to study the influence of transport current on the measured magnetization of type II superconductors. For the flux-pinned condition, it is shown that the field distribution within the sample can be described in terms of a number of regions in H−1 space. The boundaries of these regions have been established and the corresponding dependence of the magnetization on field (at fixed finite current) and current (at fixed applied field) has been calculated.