This paper presents optimization methods to design frame structures from a stock of existing elements. These methods are relevant when reusing structural elements over multiple service lives. Reuse has the potential to reduce the environmental impact of building structures because it avoids sourcing new material, it reduces waste and it requires little energy. When reusing elements, cross-section and length availability have a major influence on the structural design. In previous own work, design of truss structures from a stock of elements was formulated as a mixed-integer linear programming (MILP) problem. It was shown that this method produces solutions which are global optima in terms of stock utilization. This work extends previous formulations to stock-constrained optimization of frame structures subject to ultimate and serviceability limit states hence expanding the range of structural typologies that can be designed through reuse. Fundamental to this method is the globally optimal assignment of available stock elements to member positions in the frame structure. Two scenarios are considered: A) the use of individual stock elements for each member of the frame, and B) a cutting stock approach, where multiple members of the frame are cut from a single stock element. Numerical case studies are presented to show the applicability of the proposed method to practical designs. To carry out the case studies, a stock of elements was inventoried from shop drawings of deconstructed buildings. Results show that through reusing structural elements a significant reduction of embodied greenhouse gas emissions could be achieved compared to optimized structures made of new elements.