Traditional turbine blades have root attachments which are sites of fretting fatigue failures due to the frictional sliding of the blades during vibration. Newer integrally bladed rotors (IBR) eliminate the root attachment by manufacturing the rotor disk and blades as a unitized structure. IBRs eliminate sites of fretting fatigue failure but in doing so they also eliminate frictional damping that is provided by the root attachments. The absence of frictional damping leads to larger forced-response vibration amplitudes and premature highcycle fatigue failure in IBRs. Furthermore, IBRs also tend to exhibit blade vibrations in simultaneous multiple modes. Including these multi-mode vibration responses in estimating blade stress is critical for accurately estimating life of the blade. Conventional methods to estimate blade stresses during engine tests subjected to the forced-responses rely on vibration strain measurement techniques that measure surface strains using strain gauges. Frequency decomposition of these strain gauge data provides information on which modes are excited. The peak stress is computed using the measured strain amplitude for the particular mode and previously computed gauge factors. Strain measurement techniques are intrusive in nature and can only provide the response of the instrumented blade. Recently non-intrusive techniques such as blade tip timing (BTT) analysis have been used to measure the tip amplitude of the vibrating blade and this in conjunction with modal stresses obtained from finite element analysis can be used to estimate the peak stresses on the blade due to multi-mode excitation. This thesis demonstrates a timedomain stress superposition method, combined with a search over spatial and temporal coordinates to estimate the peak blade stresses that occur due to multi-mode excitation. A critical stress limit surface is also developed for use by test engineers in ground vibration tests to implement safety limits based on measured BTT vibration amplitudes and phase angles.