We reveal a strong elastic interaction between nonferroelastic domain walls in ferroelectric thin films. This interaction, having no analogue in bulk materials, is governed by elastic fields that are associated with the domain walls and extends to distances comparable to the film thickness. Such elastic widening of the nonferroelastic domain walls is shown to be particularly strong in common ferroelectric perovskites. The results are especially relevant for the control of domain wall propagation and the understanding of polarization dynamics.