Rotary Ultrasonic Machining (RUM) is a hybrid machining approach that combines two material removal mechanisms, namely diamond grinding and ultrasonic machining. Currently available literature mainly focuses on static parametric relationships. This paper presents preliminary results of an experimental study on some aspects of the RUM process performance, surface integrity, and dynamic process modeling. A stochastic modeling and analysis technique called Data Dependent Systems (DDS) was used to study RUM generated surface profiles and cutting force signals. 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. In addition, the difference of the major wavelength between the surface profiles for machined holes and that for machined rods was investigated. The surface variation between the entrance and exit segments of both holes and rods were also studied. Moreover, the DDS modeling approach was applied to cutting force signals collected during RUM and comparisons were made to the surface profiles results.