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Distributed acoustic sensing (DAS) is an advanced seismic acquisition technology with many advantages, such as low cost, wide frequency band, dense spatial sampling, and continuous recording. The straight optical fiber is restricted to single-component data and exhibits the lack of broadside sensitivity. To address the limitations of straight optical fiber and investigate the seismic response of multi-component DAS system, we proposed a novel first-order stress and strain-rate elastic wave equation to simulate the propagation of strain-rate wavefields. Compared to conventional particle-velocity wavefields, the simulations of three numerical examples demonstrate that the proposed equation can correctly generate elastic normal strain-rate wavefields and produce multi-component DAS data. Additionally, the simulations indicate that increasing the gauge length reduces the measurement accuracy of DAS, and a helical-wound optical fiber at a winding angle of 35.3° remains insensitive to S-wave, whereas it can clearly record S-wave at 54.7°. Furthermore, this equation can be directly implemented for multi-component DAS revers time migration (RTM) or FWI, thereby eliminating the need for traditional data conversion