Although these challenge problems deal with simple systems and their responses, the problems constitute abstractions of situations that occur in the analysis of complex physical systems which are our ultimate focus. The challenge problems contain varying mixtures of epistemic and aleatory input uncertainty in parameters of the system. The first system is given by an algebraic equation, and the second system is given by a linear ordinary differential equation. Each system is intended to provide a common focus and challenge for experimentation, discussion, and comparison of multiple approaches to the assessment and propagation of uncertainty.