Vertical drains increase the rate of consolidation in soft soils by facilitating faster dissipation of excess pore water pressure through short, horizontal drainage paths. This paper presents an analytical solution for non-linear radial consolidation under equal-strain conditions incorporating smear but ignoring well resistance. Three aspects of non-linearity are considered: (a) non-Darcian flow, (b) a log-linear void-ratio-stress relationship; and (b) a log-linear void-ratio-permeability relationship. The analytical solution to non-linear radial consolidation can explicitly capture the behaviour of both overconsolidated and normally consolidated soils. For non-linear material properties, consolidation may be faster or slower when compared with the cases with constant material properties. The difference depends on the compressibility/ permeability ratios (Cc/Ck and Cr/Ck), the preconsolidation pressure and the stress increase. If Cc/Ck < 1 or Cr/Ck < 1 then the coefficient of consolidation increases as excess pore pressures dissipate, and the corresponding rate of consolidation is greater.