Significant tensile stresses inside solid thermal energy storage media are induced due to incompatible thermal expansion characteristics. These stresses can cause damage to the often brittle storage material which is associated with a performance loss of thermal properties or the partial loss of long-term mechanical stability. In the present paper, a previously introduced analytical approach is extended to estimate the effects of the dominant physical and geometrical quantities on critical tensile stresses around tubular heat exchangers. Results are presented in terms of three composite dimensionless parameters representing the geometrical and material parameters of the system. Analytical sensitivities furthermore provide a direct quantification of how these sensitivities depend on selected system parameters, thus giving clues regarding the most promising optimisation handles. A representative case study was performed and can serve as a guide-line for making design decisions from a mechanical perspective as a complement to the typically performed thermodynamic design.