Rigorous analysis of the transient behaviour of a solid-cored magnetic circuit of rectangular section, taking into account the resistance of the magnetizing winding, is difficult to obtain and has not been attempted so far in the literature. In this paper an attempt is made to obtain, to a close degree of approximation, the transient behaviour of cores of such sections. It is shown that the complexities of the problem can be reduced by choosing certain contours of constant current density, and on this basis, four alternative solutions are obtained for the transient behaviour. These contours are justified on the basis of (a) flux decay with the magnetizing winding open and (b) eddy-current loss due to alternating flux: rigorous solutions for the two cases are available for comparison. The analysis is illustrated with a specific application to the rise of flux due to an impact excitation on a solid core, and certain conclusions are drawn.An interesting feature of the paper is that, in the majority of cases, the results are presented in a non-dimensional form.