© 2019 Elsevier B.V. Real systems are usually modeled in continuous-time by differential equations. In practice, however, we have to deal with them using discretized models and sampled data. These models, however, have more zeros than the continuous-time model. In this paper we show that there is a specific relation between these sampling zeros and the smoothness of the continuous-time input to the plant generated by a hold device using spline interpolation. On the other hand, in numerical analysis, ordinary differential equations are solved using numerical integration methods such as Runge–Kutta. In this paper we also characterize the asymptotic sampling zeros of approximate sampled-data models when using a Runge–Kutta method of a given order under uniform sampling and the input signal is obtained by spline interpolation. These results show the strong connections between the presence and characterization of sampling zeros, spline interpolation and numerical integration techniques. Moreover, the results presented in the paper provide additional insights about the impact of the details of the sampling process on the resulting discrete-time model.