The use of ultra-high performance concrete (UHPC), a stronger and more durable class of concrete, has increased in recent years. Large-scale production has been limited due to the cost of proprietary UHPC products, but the development of less expensive, non-proprietary mix designs has the potential to change that. However, this material has much larger tensile strengths than conventional concrete, in large part due to the presence of steel fibers. The traditional concrete analysis and design method of ignoring tensile strength would be overly conservative and would not accurately predict behavior. Therefore, there is a need to understand the multiaxial tensile behavior of UHPC to facilitate creating accurate analysis models and design guidelines. The purpose of this research was to develop a novel apparatus with the ability to conduct triaxial tension, biaxial tension, and tension-tension-compression testing on UHPC cube specimens. Once the apparatus, the Looney Bin, was designed and fabricated, trial tests were conducted for each of the stress conditions to develop test procedures. Then, a comprehensive set of multiaxial tension data was collected on a non-proprietary UHPC mixture with fiber contents of 0%, 1%, 2%, 4%, 5%, and 6% fibers by volume. The collected data showed that the triaxial tension strength was approximately 6.2% of the uniaxial compressive strength for fiber contents ranging from 1% to 4% and was approximately 5.8% for 0% fibers. Also, exponential decay functions were fitted to the tension-tension-compression data to estimate the reduction in compressive strength as the applied tension in two orthogonal directions increases. Lastly, the finalized multiaxial dataset was combined with previously published data encompassing the compression end of the failure surface for curve fitting. Nonlinear regression analyses were conducted to fit two separate failure surface functions to the combined dataset. Arbitrary parameters were determined for each general equation that provided the best fit to the combined dataset. The fitted equations could be implemented in analysis models to more accurately predict the strength and behavior of full-scale UHPC structural elements.