Radially convergent tracer test (RCT) with an extraction well and a tracer injection well is commonly conducted for determining aquifer dispersivity associated with the spreading of contamination plume. A variety of analytical models for RCT have been proposed, but the effects of skin zone and vertical dispersion are rarely explored. In addition, little attention is paid to the validity of those analytical models assuming asymmetrical tracer transport (ATT) as radially symmetrical transport (RST) toward the pumping well. This study develops a new analytical model for RCT subject to the above-mentioned effects in a confined aquifer with a skin zone around the wellbore. The Laplace-domain solution of the model for a continuous or instantaneous input is developed. A finite element solution (FES) for AFT is also developed to verify the Laplace-domain solution based on RST. Results suggest ATT can be regarded as RST in predicting the breakthrough curve (BTC) at the pumping well when four quantitative conditions are met. A lumped dimensionless parameter dominates those two effects on the BTC. Both the FES and Laplace-domain solution agree with monitored concentration data from a field RCT.