Burgers rheological model is used to establish the consolidation equations with the consideration of vertical and radial consolidations, while soil around pile is assumed to be saturated viscoelastic media. According to free-draining or undrained condition, the boundary condition is divided into three categories. Series solutions for dissipation of excess pore water pressure are obtained. The series solutions can provide theoretical basis for inverse calculation of consolidation coefficient from static cone penetration test. On this basis, application program is compiled to analyze the main parameters of Burgers rheological model. The result shows that the consolidation rate reduces with depth within a certain depth under the conditions of ground surface free-draining and pile tip foundation undrained. But beyond a threshold, consolidation rate tends to stabilize. When both of upper and lower boundaries are under free-draining condition, the consolidation rate with depth will decrease at first, followed by stabilizing, and increase again at the end. When both of upper and lower boundaries are under undrained condition, the dissipation rate of pore pressure no longer changes with the variation of depth, which can be considered as a special circumstance only considering vertical consolidation. Also, the rheological property has great influence on the dissipation rate of excess pore water pressure. The excess pore water pressure tends to a non-zero value with the variation of G1/η1, and the value increases with the increasing of G1/η1. When other parameters are invariant, the dissipation rate of pore pressure decreases with the increasing of G1/G2.