Solitons are simulated in an anharmonic linear lattice that is susceptible to a soft mode instability. The soft mode characteristic is introduced in the system by the addition of a term (−Au_n²) in the potential between the neighbouring atoms and the evolution of the system is studied as the soft mode parameterA varies from zero to the square of the limiting optical frequency. It is shown that the displacement pattern of the system shows three regions. First there is a region in which the relative displacements of the atoms show large amplitude oscillations. This is followed successively by a domain in which the relative displacements of the atoms are negligible and then by the soliton itself. In the soft mode region, the displacements of the atoms preceding the soliton decrease drastically in a linear fashion first, parabolically next and later become steady. It further exhibits a kind of devil’s stair cases.