Abstract: A new rigorous analytical solution is deduced from the equivalent strain governing equation for the consolidation by vertical drains on the basis of the assumption proposed by Deng et al (2013), that is, the well resistance increasing linearly with depth and exponentially with time. The solution is verified through the comparison with the results got from the existing analytical solution, in which the well resistance remains constant. Based on the new solution, the average excess pore water pressure and average degree of consolidation are compared with different rates of change of the well resistance (described by coefficient A₂ and A₃), and the influences of the depth and time-dependent well resistance on the rate of the consolidation by vertical drains are analyzed. It shows that the increase of the well resistance with depth and time will slow down the rate of the consolidation, and even make the ability of accelerating consolidation of vertical drains lose gradually.