According to the invention, there is provided a novel soybean variety designated RJS42001. This invention thus relates to the seeds of soybean variety RJS42001, to the plants of soybean RJS42001 to plant parts of soybean variety RJS42001 and to methods for producing a soybean plant produced by crossing plants of the soybean variety RJS42001 with another soybean plant, using RJS42001 as either the male or the female parent.