Polymer microfiber arrays with mushroom-shaped tips are shown to adhere well to a soft, smooth substrate. An existing model describing the effect of backing layer thickness is also shown to be applicable to the adhesion of fibrillar arrays on soft surfaces. Simulations showed that adhesion can be enhanced by increasing the compliance of the microfibers in addition to maximizing single-fiber adhesion. This model can be used to guide the development of optimized microfiber adhesives for use on soft surfaces such as biological tissues or textiles.