This paper describes a sequence of residual stress measurements made to determine a two-dimensional map of biaxial residual stress in a stainless steel weld. A long stainless steel (316L) plate with an eight-pass groove weld (308L filler) was used. The biaxial stress measurements follow a recently developed approach, comprising a combination of contour method and slitting measurements, with a computation to determine the effects of out-of-plane stress on a thin slice. The measured longitudinal stress is highly tensile in the weld- and heat-affected zone, with a maximum around 450 MPa, and compressive stress toward the transverse edges around −250 MPa. The total transverse stress has a banded profile in the weld with highly tensile stress at the bottom of the plate (y = 0) of 400 MPa, rapidly changing to compressive stress (at y = 5 mm) of −200 MPa, then tensile stress at the weld root (y = 17 mm) and in the weld around 200 MPa, followed by compressive stress at the top of the weld at around −150 MPa. The results of the biaxial map compare well with the results of neutron diffraction measurements and output from a computational weld simulation.