In this paper we study the impact of voice traffic on the performance of packet data transmission in Terrestrial Trunked Radio (TETRA) networks. Emphasis is given on the performance of applications characterized by occasionally transmitting small messages between a number of radio terminals and a fixed server, while these terminals are also conducting group voice calls. We present simulation results for practical scenarios and discuss how key performance indicators such as the delay and loss rate characteristics are affected by the group call activity of the radio terminals. Our results can help in dimensioning and planning TETRA networks, and in particular, in determining the number of packet data terminals that can be supported in a cell for a given traffic profile and QoS constraints.