Layered manufacturing (LM) processes have emerged as legitimate processes for manufacturing various precision microelectronic components and bio-implants. These processes are also being considered for fabricating large customized free forms like buildings, statues, reactor beds, and car bodies. Many of these applications demand high levels of quality (e.g., Ra<0.1μm) and functional performance. Among the LM processes, extrusion-based processes can potentially offer high production rates together with lower setup and operating costs. Yet process failures resulting from anomalies, such as nozzle clogging, overflow, dynamic instabilities, bambooing, and machine degradation impede a widespread applicability of these processes. Scientific principles that relate the sources of these anomalies to process dynamics seem necessary for effective quality monitoring. In this paper we present a nonlinear lumped-mass model to capture dynamics underlying contour crafting, which is an extrusion-based LM process. The two degrees-of-freedom model, developed based on experimental characterizations, captures salient features of the process dynamics including the prominent manifestations of process nonlinearity. Experimental investigations show that the model can lead to effective monitoring of process conditions including overflow and underflow of material from extrusion nozzle, as well as suboptimal (fast and slow) feed rates of the extrusion head.