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A good stacking method can increase the packaging utility rate and reduce production costs. Much research has focused on 2D arrangements for rectangular, circular, or irregular shapes and regularly shaped 3D objects such as rectangular boxes. Genetic algorithms, simulated annealing, and other heuristic algorithms have been proposed. Recent research on the stacking of irregular-shaped 3D stone pieces has focused on balancing one stone piece on top of others to form one or more vertical towers, given the geometry of the stone pieces and the number of stone pieces available for the task. Stacking irregular-shaped 3D objects in a package is common in industry. However, there has been relatively little emphasis on the development of algorithms for stacking irregular-shaped 3D objects in a fixed-size container without prior knowledge of the stone geometries and the number of pieces available, with the goal of packing as many stone pieces as possible while maintaining stability. In this paper, three heuristic algorithms are proposed to solve the problem of nesting irregularly shaped stone pieces in layers within a container. All three algorithms use the following approach: (1) approximate the alignment of irregular shapes to a cluster of straight lines; (2) arrange stones one by one at the approximated angles using a step-by-step process; (3) for stability, consider the weight of the stone pieces based on pixel calculations. An automated real-time stacking system—including sensors, pneumatic suction cups, webcams, conveyor, robot, and programmable logic controller—was developed to evaluate the proposed algorithms using space utilization, stability, and cycle time as measures of performance. The developed algorithms and an existing stacking algorithm (bottom left most, or BLM) were tested using 25 sequences of 30 randomly ordered stone pieces. Results suggest that the developed algorithms effectively solve the stone piece packing problem. All three were significantly better than the BLM algorithm in terms of space utilization and stability, and there was no difference in cycle time. Algorithm 3 was better than Algorithms 1 and 2. [ABSTRACT FROM AUTHOR]