The invention provides seed and plants of the tomato hybrid designated BS 01031842. The invention thus relates to the plants, seeds and tissue cultures of tomato hybrid BS 01031842, and to methods for producing a tomato plant produced by crossing a plant of tomato hybrid BS 01031842 with itself or with another tomato plant, such as a plant of another hybrid. The invention further relates to seeds and plants produced by such crossing. The invention further relates to parts of a plant of tomato hybrid BS 01031842, including the fruit and gametes of such plants.