Random matrix and free probability theory have many fruitful applications in many research areas, such as digital communication, mathematical finance and nuclear physics. In particular, the concept of free deconvolution can be used to obtain the eigenvalue distributions of involved functionals of random matrices. Historically, free deconvolution has been applied in the asymptotic setting, i.e., when the size of the matrices tends to infinity. However, the validity of the asymptotic assumption is rarely met in practice. In this paper, we analyze the additive and multiplicative free deconvolution in the finite regime case when the involved matrices are Gaussian. In particular, we propose algorithmic methods to compute finite free deconvolution. The two methods are based on the moments method and the use of zonal polynomials.