We present a method to evaluate the pion structure functions from a box diagram calculation. Pion and constituent quark fields are coupled through the simplest pseudoscalar coupling. The &ggr;*&pgr; →qq¯cross‐section is evaluated and related to the structure functions. We then show that the introduction of non‐perturbative effects, related to the pion size and preserving gauge invariance, provides us with a straighforward relation with the quark distribution. It is predicted that higher‐twist terms become negligible forQ2larger than about 2 GeV2and that quarks in the pion have a momentum fraction smaller than in the proton. We enlarge the discussion concerning this violation of the momentum sum rule, emphasizing that the sum rule is recovered in the chiral limit and also when the finite size condition is not imposed. © 2003 American Institute of Physics