•The attenuation of shear strain in the resin matrix near a buckled fiber was considered.•The nonlinear stress-strain relationship during the post-buckling process was investigated.•The classical elastic-viscoelastic correspondence principle was established to determine the dynamic buckling behaviors of SMPC at different temperatures. The microbuckling mechanics of unidirectional fiber-reinforced shape memory polymer composite (SMPC) with low fiber volume fraction were investigated, and the mechanical models were formulated considering the attenuation of shear strain in the resin matrix near the buckled fibers. We deduced the analytical expression of the attenuation function and the key parameters during the microbuckling process of SMPC, including the critical buckling wavelength and strain. The values determined by finite element analysis verified the accuracy of the above theoretical predictions. The nonlinear stress–strain relationship during the post-buckling process was also investigated. Additionally, the classical elastic–viscoelastic correspondence principle was established to determine the dynamic buckling behaviors of SMPC at different temperatures. The viscoelastic parameters of shape memory polymer (SMP) were obtained from the isothermal stress relaxation experiments, and then the variation of buckling wavelength with time at different temperatures was evaluated.