This paper studies waiting time distributions of customers in a multi-server queueing system with customer interjections and finite buffer. The customers who enter the system are divided into regular customers and interjection customers according to whether they interject the queue or not. After entering the system, the regular customers queue up at the end of the waiting line and wait for service, while the interjection customers queue up as close as possible to the head of the waiting line to receive service. By using the properties of negative exponential distribution and phase type distribution, the matrix expressions of waiting time distribution of customers in waiting queue position $n$, regular customers and interjection customers are derived. Further, the plots of waiting time distributions with time $t$ are given.