Design is the critical first step in the development of a new mRNA medicine. Informed sequence design can confer major improvements to the performance of mRNA medicines, including the strength and duration of protein expression. Here, we describe mRNArchitect (https://basefacility.org.au/software/), an open-source software platform for the optimisation of primary mRNA sequences. mRNArchitect enables the rapid assembly of mRNA sequences according to user-defined constraints, such as codon optimisation, secondary structure, GC content, and uridine depletion. mRNArchitect has been extensively validated across diverse mRNA applications, in multiple cell- and tissue types. We demonstrate that sequence optimisation with mRNArchitect increases protein expression by up to five-fold compared to alternative design methods. In addition, we identify 5′ and 3′ untranslated region (UTR) sequences that increase protein expression by up to 40% relative to benchmark UTRs. Finally, we show that incorporation of microRNA binding sites in 5′ or 3′ UTRs can decrease protein expression in off-target tissues by an order of magnitude, while retaining strong expression in target tissues. Together, our results establish mRNArchitect as a robust and flexible framework for the optimisation of mRNA expression and tissue specificity.