Machine translation has been a particularly difficult problem in the area of Natural Language Processing for over two decades. Early approaches to translation failed in part because interaction effects of complex phenomena made translation appear to be unmanageable. Later approaches to the problem have succeeded but are based on many language-specific rules. To capture all natural language phenomena, rule-based systems require an overwhelming number of rules; thus, such translation systems either have limited coverage, or poor performance due to formidable grammar size. This paper presents an implementation of an "interlingual" approach to natural language translation. The UNITRAN system relies on principle-based descriptions of grammar rather than rule-oriented descriptions. The model is based on linguistically motivated principles and their associated parameters of variation. Because a few principles cover all languages, the unmanageable grammar size of alternative approaches is no longer a problem.