The tactile sensation of stroking soft fur, known for its comfort and emotional benefits, has numerous applications in virtual reality, animal-assisted therapy, and household products. Previous studies have primarily utilized actual fur to present a voluminous fur experience that poses challenges concerning versatility and flexibility. In this study, we develop a system that integrates a head-mounted display with an ultrasound haptic display to provide visual and haptic feedback. Measurements taken using an artificial skin sheet reveal directional differences in tactile and visual responses to voluminous fur. Based on observations and measurements, we propose interactive models that dynamically adjust to hand movements, simulating fur-stroking sensations. Our experiments demonstrate that the proposed model using visual and haptic modalities significantly enhances the realism of a fur-stroking experience. Our findings suggest that the interactive visuo-haptic model offers a promising fur-stroking experience in virtual reality, potentially enhancing the user experience in therapeutic, entertainment, and retail applications.