This article considers how the principled design of interactive, computer-delivered tasks can enable the assessment of problem solving and process skills in ways that would not be possible in a conventional test. The case studied is World Class Tests, a project started by the UK government in 1999, which set out to produce and deliver summative assessment tests that would reveal “submerged talent” in 9 and 13 year-old students who were not being challenged by the regular curriculum. There were two subjects: “Mathematics” and “Problem-solving in Mathematics, Science and Technology”; 50% of the test for each subject was delivered on computer. This article describes the design and development of the computer-based tests in problem-solving, and discusses some implications for the current effort to increase the emphasis on problem-solving and process skills in assessment. The author was the lead designer for the project strand working on computer-based problem solving tasks.