Let C : Y 2 = a n X n + · · · + a 0 be a hyperelliptic curve with the a i rational integers, n ≥ 5, and the polynomial on the right-hand side irreducible. Let J be its Jacobian. We give a completely explicit upper bound for the integral points on the model C, provided we know at least one rational point on C and a MordellWeil basis for J .)ޑ( We also explain a powerful refinement of the Mordell-Weil sieve which, combined with the upper bound, is capable of determining all the integral points. Our method is illustrated by determining the integral points on the genus 2 hyperelliptic models Y .