The results of an analytical treatment of the time-dependent 2D full-waveequation are presented here for the case of ultra-short pulse (USP)reflectometry. We consider several models of the plasma geometry, namelylinear and nonlinear slab models, as well as a 2D plasma density profile withcylindrical symmetry. The latter model is more realistic when compared to the1D stratified plasma models previously employed in all the analytical, andmost numerical, treatments, since the plasma in fusion toroidal devices,mirror machines and plasma processing chambers can often be considered axiallysymmetric on the scale relevant to microwave reflectometry.Based on the results of analytical modelling, a signal record analysismethod of profile reconstruction is proposed. The method has the advantageof using raw signal records instead of poorly localizedfrequency modes, which makes it robustfor the profile measurements using USP reflectometry.