Axially compressed buckled beams have been used for several decades as elastic suspensions characterized by high static stiffness and low dynamic stiffness. The most comprehensive mathematical modelling of buckled beams is based on the elastica theory, a rational framework that seeks the equilibrium configuration for arbitrarily large deflections and rotations. The use of the elastica model is straightforward for analysis purposes but is rather awkward for design tasks because it requires handling of elliptic functions. This paper presents approximate equations developed from the elastica solution to facilitate the structural synthesis of buckled-beam suspensions starting from high-level engineering specifications. The step-by-step design procedure is illustrated by means of a case study and the theoretical predictions are validated against test data and finite element results.