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A meshless model is developed to investigate behaviors of heat conduction in skin tissues. The model is established through combined use of Laplace transform (LT), radial basis function (RBF) and method of fundamental solution (MFS). The well-known Pennes bioheat model is used to describe the process of heat conduction in skin tissues. First, Laplace transform is applied to handle the time variable in the Pennes bioheat equation, which results in a generalized Helmholtz equation. Then, a RBF-MFS scheme is constructed to solve the Helmholtz equation in Laplace space. Further, Stefest's algorithm is employed to convert the results in Laplace space back into the time space. Finally, the performance of the proposed method is assessed by several benchmark examples. The results demonstrate desirable efficiency and accuracy of the proposed method.