Fingerprints represent a particular characteristic for each individual. Characteristic patterns are also formed on the palms of the hands and soles of the feet. Their origin and development is still unknown but it is believed to have a strong genetic component, although it is not the only thing determining its formation. Each fingerprint is a papillary drawing composed by papillae and rete ridges (crests). This paper proposes a phenomenological model describing fingerprint pattern formation using reaction diffusion equations with Turing space parameters. Several numerical examples were solved regarding simplified finger geometries to study pattern formation. The finite element method was used for numerical solution, in conjunction with the Newton-Raphson method to approximate nonlinear partial differential equations. The numerical examples showed that the model could represent the formation of different types of fingerprint characteristics in each individual.