This paper presents a unified approach to the distributions of the product ofk(≥2) maximum values, and the product ofksample ranges from rectangular populations, both for equal and unequal sample sizes. The results obtained are generalisations based on some earlier work of Rider. It is proved that in all cases the distributions can be conveniently transformed to χ2's by the use of a well-known logarithmic transformation. It is also suggested that these results might be of use in quality control procedures in high precision production engineering with close specification limits.