According to the invention, there is provided a novel soybean variety designated 98R31. This invention thus relates to the seeds of soybean variety 98R31, to the plants of soybean 98R31 to plant parts of soybean variety 98R31 and to methods for producing a soybean plant produced by crossing plants of the soybean variety 98R31 with another soybean plant, using 98R31 as either the male or the female parent.