We present 3D dynamic Monte-Carlo simulations of the growth of an actin network close to an obstacle coated with Wiskott-Aldrich syndrome protein (WASP), an inducer of actin branching. Our simulations incorporate both elasticity and relaxation of the actin tail, thus allowing for local network compression. Whilst steady state motility derives mainly from polymerization at the leading edge, nonthermal stored elastic energy and retrograde flow are observed in a thin slab of material close to the obstacle. We observe a crossover from steady to hopping bead motion as the branching rate is decreased.