Structural relaxations in electronically excited poly(para-phenylene) are studied using many-body perturbation theory and density-functional-theory methods. A sophisticated description of the electron-hole interaction is required to describe the excitonic energies, but the associated structural relaxations can be obtained quite accurately within a constrained density-functional-theory approach. We find that the structural relaxations in the low-energy excitonic states extend over about eight monomers, leading to an energy reduction of 0.22 eV and a Stokes shift of 0.40 eV.