The basic principles governing the development and function of living organisms remain only partially understood, despite signifificant progress in molecular and cellular biology and tremendous breakthroughs in experimental methods. The development of system-level, mechanistic, computational models has the potential to become a foundation for improving our understanding of natural biological systems, and for designing engineered biological systems with wide-ranging applications in nanomedicine, nanomaterials and computing. We describe Z34Bio (Z3 for Biology), a unified SMT-based framework for the automated analysis of natural and engineered biological systems. Z34Bio enables addressing important biological questions, and studying models more complex than previously possible. The framework provides a formalization of the semantics of several model classes used widely for biological systems, which we illustrate through the treatment of chemical reaction networks and Boolean networks. We present case-studies which we make available as SMT-LIB benchmarks, to enable comparison of different analysis techniques, and towards making this new domain accessible to the formal verification community.