A snap-on attachment structure for attaching a side skin to an upright frame of a wall system. The attachment structure includes resilient attachment strips secured to the rear of the skin and extending along upright edges thereof. Each strip cooperates with a projection formed on an upright frame member and extending vertically therealong. The snap-on strip has a pair of cantilevered spring legs which protrude outwardly in angled relationship. The spring legs adjacent outer ends are provided with coil-shaped head parts which protrude inwardly toward one another. The head parts have hollow arcuate configurations and move into gripping engagement with shallow arcuate recesses formed on opposite sides of the projection.