Starting in the middle of November 2002, the CMS experiment undertook an evaluation of the European DataGrid Project (EDG) middleware using its event simulation programs. A joint CMS-EDG task force performed a stress test by submitting a large number of jobs to many distributed sites. The EDG testbed was complemented with additional CMS-dedicated resources. A total of ~ 10000 jobs consisting of two different computational types were submitted from four different locations in Europe over a period of about one month. Nine sites were active, providing integrated resources of more than 500 CPUs and about 5 TB of disk space (with the additional use of two Mass Storage Systems). Descriptions of the adopted procedures, the problems encountered and the corresponding solutions are reported. Results and evaluations of the test, both from the CMS and the EDG perspectives, are described.