High-order perturbation solutions have been obtained for the simple physical model describing the LH2 spreading with a continuous spill, and are shown to improve over the first-order perturbation solutions. The non-dimensional governing equations for the model are derived to obtain more general solutions. Non-dimensional parameters are sought as the governing parameters for the non- dimensional equations, and the non-dimensional evaporation rate is used as the perturbation parameter. The results show that the second-order solutions exhibit an improvement over the first- order solutions with respect to the pool volume; however, there is still a difference between numerical solutions and second-order solutions in the late stage of spread. Finally, it is revealed that the third- order solutions almost agree with numerical solutions.