Characterizing soft, biological materials in the high strain rate regime (> 104 s−1) is crucial to make accurate predictions of the dynamics of such materials under blast loadings. The inertial microcavitation rheometry (IMR) technique is able to characterize soft materials in this regime by minimizing the error between a spherical bubble dynamics model and experiments of laser-induced cavitation (LIC) bubbles [1]. However, doing so has been challenging due to limited optical access and non-spherical bubble surface perturbations. We consider a bubble with non-spherical equilibrium and current configurations in a transversely isotropic viscoelastic material. The coordinate mapping between the two configurations is linearized about small surface perturbations in both frames. We consider a Kelvin-Voigt model for the elastic and viscous contributions to the Cauchy stress tensor with a Newtonian viscous contribution. The elastic contribution is modeled using a quadratic standard reinforcing model. From momentum balance, we obtain second-order ordinary differential evolution equations for each mode bubble surface perturbation amplitude. To validate the model, we conduct two different microbubble experiments: (i) ultrasound-forced small radial oscillations and (ii) LIC large radial oscillations, and numerical finite element simulations. The transverse isotropic materials are 3D printed resin gels with stiffer fibers encased in a softer matrix, resembling biological tissues. The bubble’s surface perturbations from experiments are extracted using spectral interpolation and serve as objectives to identify the material parameters. We report the optimal material properties and show agreement with the experiments. Because the model relies on solutions to ordinary differential equations, the inverse characterization process (involving hundreds of simulations) runs locally on the order of tens of minutes, compared to a single simulation of non-spherical bubble oscillations in water which can exceed 48 hours of runtime on 48 CPU cores [2]. [1] Estrada J. B., Barajas C., Henann D. L., Johnsen E., Franck C., High strain-rate soft material characterization via inertial cavitation, Journal of the Mechanics and Physics of Solids, Vol. 112, 2018. [2] Nagy D., Adami S., Heged˝us F., Direct numerical simulation of spherical and non-spherical bubble dynamics using the ALPACA compressible multiphase flow solver, International Journal of Multi-phase Flow, Vol. 191, 2025