In this work, we analyse the dynamics of a discretized version of a continuous system modelling somitogenesis examined by Kovács et al. (Oscillations in a System Modelling Somite Formation. In: Mondaini, R.P. (ed.) Trends in Biomathematics: Stability and Oscillations in Environmental, Social, and Biological Models, pp. 237–248. Springer International Publishing (2022)). The explicit Euler scheme and a nonstandard finite difference scheme is constructed to transform the continuous-time system into the discrete-time model. Firstly, we discuss basic properties of the discrete system, such as boundedness of variables and positivity of solutions. We investigate whether the new discrete-time model shows dynamic consistency with its continuous counterpart.