This paper proposes a new mathematical framework for the open pit mine planning problem, based on continuous functional analysis. The main challenge for engineers is to determine a sequence of nested profiles maximizing the net present value of the mining operation. The traditional models for this problem have been constructed by using binary decision variables, giving rise to large-scale combinatorial and Mixed Integer Programming problems. Instead, we use a continuous approach which allows for a refined imposition of slope constraints associated with geotechnical stability. The framework introduced here is posed in a suitable functional space, essentially the real-valued functions that are Lipschitz continuous on a given two dimensional bounded region. We derive existence results and investigate qualitative properties of the solutions.