In this paper, we investigate and evaluate origami and kirigami patterns that enable folding arrays made from flat rigid panels with uniform thickness into compact stacks. In deployed state, all panels form a completely flat plane; while in folded state, no voids exist within the stack. Two approaches are proposed. The first approach folds an array of identical rectangular panels into compact stacks. By drawing a Hamiltonian circuit over the array, a method of placing revolute joints is presented. By selecting a symmetric Hamiltonian circuit, we show that the array can be folded into two stacks. The second approach is case specific, which folds arrays consisting of square and half square triangular panels into stacks. Three basic units as well as their combinations are proposed, all of which lead to compact folding. Our designs can be applied to package solar panels for aerospace applications.