Grant-free non-orthogonal multiple access (NOMA) has been regarded as a key-enabler technology for ultra-reliable and low-latency communications (URLLC). In this paper, we analyse the performance of NOMA with short packet communications for URLLC. In this regard, the overall packet loss probability consists of transmission error probability and queueing-delay violation probability. Queueing-delay has been modelled using the effective bandwidth. Due to short transmission time, the infinite block-length has been replaced with finite blocklength of the channel codes which rules out the application of Shannon's formula. The achievable effective bandwidth of the system is derived, and then, the transmission error probability has been analysed. The derivations are validated through extensive simulations, which shows the variations of the signal-to-noise ratio (SNR) requirements of the system for various transmissionerror probability, QoS exponent, and the transmission packet size.