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Actuation devices made of smart polymers typically show various instabilities, which can adversely affect their performance and lead to device failure. In general, smart polymers exhibit wrinkling instability when subjected to an electric or magnetic field. At the same time, wrinkles can be used constructively in certain applications demanding a controlled alternation of the surface morphology. Critical factors influencing thin films' pull-in and wrinkling instabilities are discovered concerning the anisotropic taut domains with an applied electro-magneto-mechanical field control. A continuum mechanics-based electro-magneto-mechanical model is developed for predicting the thresholds on the taut domains in the plane of principal stretches. Also, the concept of natural width under simple tension is implemented to derive the coupled nonlinear equation that evaluates the associated taut domains. The findings of the model solution indicate that the extent of taut domains can be controlled by modifying the level and the principal direction of the transverse isotropy. Additionally, the taut domain for a particular level of applied electromagnetic field increases with an increase in the anisotropy parameter, while it depleted with an increase in the fiber orientations from 0 ° to 90 ° for an applied level of electromagnetic loading. • A taut domains model of electro-magneto-active smart thin membrane is developed. • The concept of natural width in tension is applied to derive the governing equation. • The proposed model is validated with an energy-based model of dielectric membrane. • The effect of anisotropy and fiber orientations on the taut domains is investigated. [ABSTRACT FROM AUTHOR]