Systems and methods are provided for use in assessing the stability of simultaneous machining (SM) dynamics (which is also known as parallel machining). In SM, multiple cutters, which are generally driven by multiple spindles at different speeds, operate on the same work-piece. In an alternative implementation of SM, single milling cutters with non-uniformly distributed cutter flutes operate on a work-piece. When SM is optimized in the sense of maximizing the rate of metal removal constrained with or by the machined surface quality, “chatter instability” phenomenon appears. The present disclosure declares the complete stability picture of SM chatter within a mathematical framework of multiple time-delay systems (MTDS). A cluster treatment of characteristic roots (CTCR) procedure determines the regions of stability completely in the domain of the spindle speeds for varying chip thickness, thereby replicating the well-known “stability lobes” concept of STM for simultaneous machining.