A viscoelastic foam system is provided having an amine-based polyoxypropylene extended polyol to impart strength, recoverability and endurance to the foam, and an appropriately selected non-amine-based polyol to provide flexibility to the foam. The combination of amine-based propylene oxide extended polyol and non-amine-based polyol provides a viscoelastic semi-rigid foam with excellent impact and recovery properties, recovering to substantially 100% of its initial volume and shape following an impact, yet with sufficient rigidity and stiffness so that it is effective at absorbing multiple impacts. A method of making the above viscoelastic foam is also provided.