In today’s digital world, no one and nothing is safe from potential cyberattacks. There is also no 100% protection from such attacks. Therefore, it is advisable to carry out various studies related to the effects of the different cyberattacks on the performance of the specific devices under attack. In this work, a study was carried out to determine how individual TCP DoS attacks affect the parameters of VoIP (Voice over IP) voice and video streams. For the purpose of this work, a model of a simple IP network has been created using the GNS3 IP network-modeling platform. The VoIP platform used was Asterisk Free PBX. Tools from Kali Linux were used to implement the individual TCP DoS attacks; IP-network-monitoring tools and round-trip-delay-measurement tools were also used. The proposed study is applicable to multiple VoIP platforms wherein voice and video traffic are passed/processed by the VoIP server. From the obtained results, it was found that Asterisk Free PBX is very well secured against TCP DoS attacks, which do not affect the platform performance or the parameters of the voice and video streams. The values of the observed parameters, such as jitter, packet loss, round-trip delay, etc., are very far from the maximum allowable values. We also observed a low load on the CPU and RAM of the system during the whole study.