Rotary ultrasonic machining (RUM) is a hybrid machining approach that combines two material removal mechanisms, namely, diamond grinding and ultrasonic machining. This paper presents the results of dynamic process modeling for RUM of alumina, as currently available literature mainly focuses on static parametric relationships. A stochastic modeling and analysis technique called data dependent systems (DDS) was used to study RUM generated surface profiles and cutting force signals. Variations in the data sets of surface profiles, for the entrance and exit segments of machined holes and for that of machined rods, and cutting force signals were modeled and decomposed to gain insight into the RUM process mechanism. The DDS wavelength decomposition of the surface profiles suggested that the major characteristic root wavelength had a positive correlation with feed rate, and the wavelength magnitude may be linked to the grain size of the workpiece material. The roughness of machined surfaces increased as the tool moved deeper due to reduced flushing efficiency. Surfaces on the machined rods were less sensitive to the input variables than the hole surfaces. Moreover, spindle speed and feed rate affected the cutting force significantly.