This paper presents the offline Virtual Network Function Packing (VNF-P) problem, a new challenging optimization problem that telecom operators face when designing the cloud infrastructure to host virtual network functions, especially in the context of 5G networks deployment. The VNF-P problem is a generalization of the classical Bin Packing Problem, where VNFs are packed onto physical servers, while taking into account capacity constraints, variable bin size and cost, conflicts between items and between items and bins, some unsplittable items, and two-compartment bins. Our contributions to this problem include a formal definition of the VNF-P problem, exact procedures and heuristic algorithms to solve it. An efficient algorithm, providing a good quality lower bound by solving a relaxation of the problem, is also provided. Numerical experiments on realistic instances were conducted in order to compare the different approaches. They show that the classical results of the literature cannot be extended naturally to this variant. The proposed algorithms have been validated on real use-case studies at Orange, and have been embedded in an operational tool to design the future cloud infrastructure.