When a human crinkles or scrunches a fragile object, for which the yield force is very small that it is hardly perceived, they identify the material of the object based on tactile stimuli delivered to the skin. In addition, humans are able to recognize materials even when they are crinkled at different speeds. In order to realize these human recognition features of the crinkle of a fragile object, we develop a vibrotactile synthesis method. This method synthesizes the vibrotactile acceleration stimuli in response to a crinkle speed based on the preliminarily measured acceleration spectra. Using this method, we develop an active footstep display that presents a virtual crinkle of fragile structures made of different materials to its users. Experimental participants could identify three of the four types of virtual structure materials at rates significantly higher than the chance level. The four materials were copy and typing paper, aluminum foil, and polypropylene film. Furthermore, the trends of answer ratios exhibit good correspondence with those for the real cylindrical fragile objects. We conclude that the developed method is valid for the virtual crinkle of fragile structures and will enhance the validity of virtual reality systems, such as a virtual walkthrough system.