This volume represents the findings of the first test cases considered by ERCOFTAC (European Research Consortium on Flow Turbulence and Combustion). 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; axisymmetric confined jet flows. These test cases represented the interests of both the academic and industrial groups in finding out the limits of various models and codes to predict real problems supported by experimental data. The articles summarise the work of each group and point to refinements and further study to perfect the models. As such there will be much of interest to all professionals and researchers concerned with the prediction of flows and turbulence.