Hidden order may arise in strongly correlated systems even if there is an apparent lack of long-range order as measured by local order parameters. This phenomenon has been essentially associated with topological order in quantum systems. Here, we demonstrate the emergence of hidden order in a 1D non-linear classical mechanical system that supports rotational degrees of freedom. The potential energy of the model system creates a bistable system for which hidden order emerges with the introduction of a biquadratic term. To our surprise, we discover that varying the strength of the biquadratic term leads to four distinct phases quantified by the behaviors of the Néel and string order parameters. Three of these phases are locally disordered. Hidden order is identified by a string order parameter that shows correlations with significantly longer range than the Néel order parameter. The hidden order correlation length diverges as the kinetic energy of the system is lowered with a critical exponent ~0.5. The observation of hidden order in a mechanical system reveals that instability and non-linearity may play critical roles in the generation of nonlocal long-range correlations in apparently locally disordered systems.