In this study, we primarily look into the contact interaction between haptic feedback devices and virtual environments which include very flexible systems. Haptic feedback devices function at relatively high frequencies, making real-time simulation of the virtual environments, which may include flexible systems, a challenge. To address this challenge, we propose to use a method based on the reduced interface model (RIM) concept. This approach was proven highly successful in applications which includes application of RIM with haptic feedback device for steering wheel, and also in other complex contact modelling scenarios. The RIM concept has generally been proven efficient for enhancing the explicit co-simulation of multibody systems in complex multirate simulation environments. It approximates the responses of the subsystems with representative reduced models during a micro time step, reducing the instability and inaccuracies in the results. As its core, the RIM represents the dynamics of the mechanical system in the contact subspace. In this work, first we present a method for computing the RIM for flexible mechanical systems represented based on the Absolute Nodal Coordinate Formulation (ANCF). We will employ that to obtain stable contact interaction between the haptic feedback device and 3-dimensional ANCF elements modelling highly flexible virtual environments. Results show stable haptic contact force rendering of the interactions with simulations running at 30-60 Hz and haptic device operating at frequencies higher than 4 KHz.