This paper considers the problem of robust stability for linear systems with a constant time-delay in the state and subject to real convex polytopic uncertainty. Both delay-independent and delay-dependent stability conditions are characterized by linear matrix inequalities which allow the use of parameter-dependent Lyapunov functionals to analyse the system stability against parameter perturbations, and therefore improve the conservativeness resulting from the single Lyapunov functional. In order to determine the maximum of time-delay within which the system remains stable, the problem can be cast into a generalized eigenvalue problem and solved by standard LMI solvers. Two examples are included to illustrate the proposed method.