This paper presents a technique to model statically indeterminate forces based on stiffness matrices for multi-limbed climbing robots. Current wall climbing robots in literature overlook statically indeterminate forces, causing an incapability to estimate climbing failure under certain circumstances. Accounting for these forces, robot deformation can be approximated, paving the way for the proposed two-wall climbing approach. During a wall climb, two failure modes, slide and over-torque, are identified to compute feasible climbing region. A hexapod robot is used to verify the proposed technique by climbing between walls with pure friction end effectors.