The present article describes measurement uncertainty estimation of a Gauge Block (GB) through the Law of propagation of uncertainty (LPU) and Monte Carlo Simulation (MCS) as per JCGM 100 and 101: 2008 recommendations respectively. This paper describes the implementation of the Monte Carlo Simulation Method (MCM) for measurement uncertainty evaluation through octave and R programming, environment for numerical computations. In the present investigation, the measurement uncertainty obtained using the GUM approach is compared with the theoretically simulated results obtained for MCM in octave and R programming. A good agreement has been observed between values obtained for expanded measurement uncertainty using these approaches.