Numerical studies for a structural dynamic system are performed in Matlab and Simulink environments. Six different earthquakes filtered and corrected using Seismosignal software, are used as seismic loads during implementation. In the first part of this study, the fourth order Runge-Kutta based Matlab code (RK4M) and Simulink Model-Based Design (SMD) are appropriately developed. Both RK4M and SMD are used to solve the governing equations for single storey structure isolated by Lead Core Rubber Bearing (LCRB). The second part compares the developed modelling methods in terms of outputs’ accuracy and Time of Implementation (TI). It is shown that both methods agree well in terms of resulting floor accelerations and displacements with slight but justifiable average differences of only 1.3 and 0.98 % respectively; thus, indicating that any of these techniques can be adopted. However, concerning TI, it is observed that SMD is in general quicker to display results as compared to the developed RK4M, which is approximately 58s longer. This leads to suggesting that SMD can be more effective, particularly for earthquakes with long-duration, and most importantly for cases where time is a governing factor during implementation. Besides, long-period and long-duration earthquakes are observed to have particular influence on structural behaviour. This reveals a need for special consideration requirements that are currently not taken into account.