This volume contains the proceedings of the 1st International Workshop on Methods and Tools for Rigorous System Design (MeTRiD 2018), held on the 15th of April, 2018 in Thessaloniki, Greece as part of ETAPS 2018, the European Joint Conferences on Theory and Practice of Software. The term "Rigorous System Design" (RSD) denotes the design approach that is based on a formal, accountable and iterative process for deriving trustworthy and optimised implementations from models of application software, its execution platform and its external environment. Ideally, a system implementation is derived from a set of appropriate high-level models by applying a sequence of semantics-preserving transformations. The ambition of MeTRiD is to promote the use of formal methods, in general, and the RSD approach, in particular, in the industrial applications and, reciprocally, bring the attention of the formal methods researchers to such industrial applications in order to develop realistic case-studies and guide the evolution of tools. Striving towards this ambitious goal, we have solicited contributions of three types: - regular papers, presenting original research - case study papers, reporting the evaluation of existing modelling, analysis, transformation and code generation formalisms and tools on realistic examples of significant size - tool papers, describing new tool prototypes supporting the RSD flow and enhancements of existing ones We have received 13 submissions (7 regular, 4 tool and 2 case study papers), whereof 8 have been accepted for presentation at the workshop: - 5 regular papers - 2 tool papers - 1 case study paper In this volume, these papers are complemented by an invited paper by Joseph Sifakis.