AbstractIn this paper we study the tail behaviour of the probability of ruin within finite time t, as initial risk reserve x tends to infinity, for the renewal risk model with strongly subexponential claim sizes. The asymptotic formula holds uniformly for t∈[f(x), ∞), where f(x) is an infinitely increasing function, and substantially extends the result of Tang (Stoch. Models 2004; 20:281–297) obtained for the class of claim distributions with consistently varying tails. Two examples illustrate the result. Copyright © 2008 John Wiley & Sons, Ltd.