A novel use of the spectral method to determine excess pore water pressure during vertical consolidation of multi-layered soil with time constant material properties is presented, considering a unit cell with combined vertical and radial drainage. Equal strain conditions are assumed in the analysis. The novel adoption of material properties that vary in a linear fashion with depth allows arbitrary distributions of properties to be modelled. By incorporating surcharge and vacuum loading that vary with both depth and time, a wide range of consolidation problems can be analysed. The spectral method is a meshless approach producing a series solution to the consolidation problem based on matrix operations. Accuracy can be improved by increasing the number of terms used in the series solution. The model is verified by the analysis of selected case studies characterised by: analytical free strain consolidation with thin sand layers (surcharge only); laboratory test and embankment trial with surcharge and vacuum loading; and ground subsidence caused by groundwater pumping.