An exact examination of a one-dimensional (1D) anharmonic elastic model describing the thermodynamic properties of spin-crossover (SCO) solids is presented. This elastic model incorporates both intra-chain and mean field inter-chain interactions, providing a more understanding of 1D SCO materials. Numerical findings for a linear chain of spins unveil intriguing features, such as a two-step-like transition. Extending the model to interacting chains leads to an additional term in the effective ligand field of the system’s Hamiltonian, thereby enhancing its predictive power by accounting for more elastic constants of interactions. This augmentation reinforces the model’s validity in capturing the spin-crossover phenomenon. Numerical results in this extended framework elucidate clearer two-step-like spin crossover transitions, with the HS_LS fraction of spins approaching maximum values at equilibrium temperature T e q .