This analysis for thermoforming triangular troughs focuses on the manufacturing process speed and follows the method of Kershner and Giacomin for thermoforming cones. We distinguish between what happens before and after (free versus constrained forming) the melt touches the prismatic mold. Neither free nor constrained forming yields analytical solutions for the required forming time. Our analysis is restricted to the fabrication of triangular troughs from nearly Newtonian melts, the second simplest relevant problem in commercial thermoforming. The simplest relevant problem, thermoforming cones, yielded analytical solutions for the forming time. Whenever we thermoform straight edges into rigid packaging, the problem of a melt stretching into a triangular trough arises. POLYM. ENG. SCI., 49:189-199, 2009. (C) 2008 Society of Plastics Engineers