A new accelerated technique, called the stepped isostress method (SSM), is presented that allows accelerated testing of materials to determine their creep response, and in particular, their creep-rupture behaviour. The approach in SSM testing is similar to the more familiar stepped isothermal method (SIM) but the acceleration is now obtained by increasing the stress in steps rather than stepping the temperature. Additional stress provides energy to the system in an analogue of the effect of heat in SIM. This method relies on the time-stress superposition concept. Various theories, assumptions and the different steps of the method are described in detail. This method is advantageous when compared with SIM because there is no need to use elevated temperatures, which may affect the chemical properties of the tested materials. The applicability of this method is investigated. The paper presents testing on Kevlar 49 yarns using SSM. The resulting creep curves and rupture times are compared with those obtained from SIM and conventional creep testing carried out in the past. The results show good correlation between the three test methods. The ability to carry out reliable creep tests in a reasonable time at low stress levels allows a designer to have much more confidence in the data for creep-rupture behaviour for fibres and allows confident prediction of structural lifetimes.