Due to widespread adoption of mobile communications devices and increasingly high throughput capacity of cellular networks, Third-Generation (3G) and Long Term Evolution (LTE) are becoming ever more popular. Millions of smart phones with 3G capabilities are sold every year and used for mostly browsing the Internet. Hence, mobile operators have been heavily investing in their packet switched networks to meet customer demand and stay ahead in the market. The widespread use of broadband mobile Internet bring along also some IP based threats such as the Denial of Service (DoS) attacks, botnets and malwares. In this paper, we performed DoS and flooding attacks on 3G mobile networks and measured their effect on the most critical elements of a network such as the Radio Network Controller (RNC) and the Serving GPRS Support Node (SGSN) devices. We carried out our experiments on a real mobile network, not just a simulation environment, and hence our findings depict a realistic picture of the vulnerabilities existent in 3G mobile networks. We propose alternative solutions to avoid these vulnerabilities and mitigate the issues raised.