Flow-state transitions in granular materials constitute an important problem in nonequilibrium statistical physics and granular physics, and are closely related to geophysical hazards such as landslides, snow avalanches, and debris flows. In particular, the transition of a granular pile from intermittent collapse to continuous steady flow is widely regarded as a key step in the initiation and evolution of many natural hazards. Although previous studies have shown that this transition is governed by factors such as particle size, friction, shape, and boundary conditions, the role of particle elastic modulus in modulating the transition threshold remains insufficiently understood.In this work, we combine rotating-drum experiments with matched numerical simulations to systematically investigate the transition from a hysteretic state to steady flow in monodisperse granular systems by varying particle radius and material elastic modulus. By tuning the drum rotation rate and employing high-speed imaging together with image-processing techniques, we extract key dynamical quantities such as the free-surface inclination angle. Based on these measurements, we introduce a dimensionless deformation parameter associated with differences in material modulus, and further propose a modified Froude number, denoted as Fr^**, that explicitly incorporates elastic-modulus effects.Our results show that, for systems with different particle sizes and elastic moduli, the transition thresholds are significantly scattered when expressed in terms of the conventional Froude number. In contrast, when recast in terms of the modified Froude number Fr^**, these thresholds collapse onto a unified criterion. In other words, the transition from the hysteretic regime to continuous steady flow can be described by a single dimensionless parameter that simultaneously accounts for inertia, gravity, and elastic deformation.These findings demonstrate that particle elasticity plays a systematic and quantifiable role in granular flow-state transitions. The proposed modified criterion provides a foundation for establishing a unified predictive framework for critical conditions, improves the practical applicability of hazard-threshold estimation, and offers experimental support for understanding the nonequilibrium rheology and constitutive behavior of granular media.