This volume represents the findings of the first test cases considered by ERCOFTAC. The workshop, held in Lausanne, Switzerland, in 1990, studied five test cases: boundary layer in an S-shaped duct; periodic array of cylinders; transition in a boundary layer under the influence of free-stream turbulence; predictions of an axisymmetric jet flow in a diverging duct; and predictions of the turbulent flow in an axisymmetric geometric configuration. These cases represented the interests of both the academic and industrial groups in determining the limits of various models and codes to predict real problems supported by experimental data. The articles summarize the work of each group and point to refinements and further study to perfect the models.