Abstract: In-situ stress is a core factor controlling dynamic gas disasters in coal mines. Existing in-situ stress models are primarily based on the elastic properties of coal-rock formations and are not suitable for viscoelastic coal media. There is a need to establish an in-situ stress distribution model suitable for viscoelastic coal properties. Coal seams, especially tectonic coal, exhibit significant creep and stress relaxation characteristics. In this study, a Fractional Maxwell stress relaxation mathematical model was developed for viscoelastic coal reservoirs. The stress component of the extended Eaton model was improved to account for the stress relaxation in viscoelastic coal seams and an in-situ stress distribution model was established for viscoelastic coal seams. The results indicate that over geological time scales, viscoelasticity significantly affects the differential stress in coal seams. The degree of coal body creep and stress relaxation increases with the increase in viscosity coefficient and fractional order factor. As the elastic modulus decreases, the Poisson’s ratio, tectonic ratio, and gas pressure increase. The stress characteristics of coal seams exhibit a trend of hydrostatic pressure state distribution. Among them, the elastic modulus and Poisson's ratio contribute significantly to the difference between vertical principal stress and horizontal stress. The tectonic ratio contributes significantly to the difference between horizontal stresses. Gas pressure contributes equally to all three principal stresses. The stress relaxation effect can alter the relative magnitudes of maximum and minimum horizontal principal stresses and reduce stress anisotropy. Based on the critical stress model, a reduction in friction coefficient and an increase in gas pressure were similarly observed in coal seams under different in-situ stress conditions, leading to an approach towards hydrostatic pressure distribution. The mechanical properties of tectonic coal are more conducive to approaching hydrostatic pressure states over geological time scales. The application of the in-situ stress model established in this study validated the field measurements and provided new insights into gas enrichment and permeability reduction in tectonic coal.