This work proposes the design and optimization of the multi-rod (≥6 rods) supporting system for cryogenic devices under variable loads. The case study of a carbon ion gantry for medical treatments has been used as an application example for the developed models. Cryogenic devices require to solve a set of engineering challenges that are unique for these applications. One of the mechanical challenges is represented by the supporting system of the device. On one hand, the supporting system must be as stiff as possible to guarantee accuracy under variable loading conditions, reacting to high variable loads related to the rotation in the case of the gantry. On the other hand the supporting system represent a direct connection between the room temperature environment and the cryogenic device cooled at cryogenic temperatures (−268.5 ◦C) transferring heat to the cooled components. This represent a cost to keep the system functional at nominal temperatures as the heat must be extracted. The design of supports, their material and their arrangement play a key role in guaranteeing high stiffness and low heat-loads and costs. No documented evidence has been found regarding the mathematical formalization of design of supporting systems for cryogenic devices subject to highly variable loads. While most common applications rely on statically indeterminate solutions under static loads, there is no documented knowledge on the potential use of a statically determinate supporting system for variable loads. This work proposes the design and optimization of two supporting systems based on supporting bars, covering both the statically determinate and indeterminate solutions and comparing them using the gantry application as a study case. Both architectures have been mathematically described by so called Lumped Parameter Models (LPMs). These models enable to study the effect of a generic load, pre-load, cooling process, backlash and vacuum on the position and orientation of the cryogenic device and the stress state of the supports. For the statically indeterminate case a generic formulation of the model has been developed, applicable to solutions with any number of supports and without pre-imposed symmetries. This formulation represents an extremely valuable result of this work regarding the applicability to a much greater number of applications. The models have been benchmarked against a widely used Finite Element Analysis (FEA) software proving the results of the developed LPMs to differ of only 1–3%. The developed models have been demonstrated to be 20 times faster than FEA in providing the same results, unlocking the full potential of computer aided optimization codes that would have been much more computationally expensive otherwise. A genetic optimization routine based on the developed LPMs have been presented and used to optimize both statically determinate and indeterminate supporting systems in the case study of the gantry. On average, the accuracy of the systems during rotation has been improved by 16% and heatloads reduced by 44% with respect to initially proposed solutions. The necessity of preload to remove backlash has been demonstrated, improving the accuracy matching the requirements, otherwise not satisfied for the system with backlash. A comparison of different materials and size of supports has been done thanks to the LPMs enabling to find the optimal material for each of the supporting systems. Finally 1 the two designed and optimized supporting systems have been compared. A qualitative parameter in the comparison considered is the possibility of automating the positioning of the cryogenic device thanks to the designed supporting system. Results show that, assuming no automation of the supporting system, the statically indeterminate solution performs overall better in terms of positional accuracy during operation, minimal heatflux and safety margin over transportation/handling loads while no major difference has been found analyzing the natural frequencies of the two solutions. In case of automation of the supporting system, the developed statically determinate solution represent a better candidate, allowing to recover elastic deformations also of the gantry main structure ultimately allowing to reduce its mass.