The purpose of this thesis is to show how to use vulnerability testing to identify and search for security flaws in networks of computers. The goal is partly to give a casual description of different types of methods of vulnerability testing and partly to present the method and results from a vulnerability test. A document containing the results of the vulnerability test will be handed over and a solution to the found high risk vulnerabilities. The goal is also to carry out and present this work as a form of a scholarly work. The problem was to show how to perform vulnerability tests and identify vulnerabilities in the organization's network and systems. Programs would be run under controlled circumstances in a way that they did not burden the network. Vulnerability tests were conducted sequentially, when data from the survey was needed to continue the scan. A survey of the network was done and data in the form of operating system, among other things, were collected in the tables. A number of systems were selected from the tables and were scanned with Nessus. The result was a table across the network and a table of found vulnerabilities. The table of vulnerabilities has helped the organization to prevent these vulnerabilities by updating the affected computers. Also a wireless network with WEP encryption, which is insecure, has been detected and decrypted.