The paper presents a numerical simulation of the first-order phase transition in the 2d 10-state Potts model using a multicanonical algorithm. The algorithm is designed to enhance configurations dominated by the presence of interfaces, which are exponentially suppressed in the canonical ensemble. The tunneling time between metastable states increases as $ L^{2.65} $, leading to a computational effort proportional to $ V^{2.3} $. This is significantly faster than the standard heat bath algorithm, which shows exponential slowing down. The multicanonical algorithm allows for a high-precision computation of the interfacial tension. The paper demonstrates that the algorithm can efficiently sample configurations in the metastable region, overcoming the critical slowing down problem for first-order transitions. The interfacial free energy is determined with high precision, yielding $ F^{s} = 0.09822 \pm 0.00079 $. The algorithm is shown to be significantly more efficient than the heat bath algorithm, with a ratio of efficiency of about 500 for the largest lattice. The results suggest that the multicanonical algorithm is a powerful tool for simulating first-order phase transitions in statistical mechanics and field theories. The paper also discusses potential applications of the algorithm to other numerical calculations in statistical mechanics, such as spin glass simulations and estimates of the free energy. The multicanonical algorithm is implemented for non-Abelian gauge theories and is expected to be useful for studying the QCD deconfining phase transition. The paper concludes that the multicanonical algorithm provides a significant improvement over standard algorithms for first-order phase transitions, particularly for systems with strong first-order transitions.The paper presents a numerical simulation of the first-order phase transition in the 2d 10-state Potts model using a multicanonical algorithm. The algorithm is designed to enhance configurations dominated by the presence of interfaces, which are exponentially suppressed in the canonical ensemble. The tunneling time between metastable states increases as $ L^{2.65} $, leading to a computational effort proportional to $ V^{2.3} $. This is significantly faster than the standard heat bath algorithm, which shows exponential slowing down. The multicanonical algorithm allows for a high-precision computation of the interfacial tension. The paper demonstrates that the algorithm can efficiently sample configurations in the metastable region, overcoming the critical slowing down problem for first-order transitions. The interfacial free energy is determined with high precision, yielding $ F^{s} = 0.09822 \pm 0.00079 $. The algorithm is shown to be significantly more efficient than the heat bath algorithm, with a ratio of efficiency of about 500 for the largest lattice. The results suggest that the multicanonical algorithm is a powerful tool for simulating first-order phase transitions in statistical mechanics and field theories. The paper also discusses potential applications of the algorithm to other numerical calculations in statistical mechanics, such as spin glass simulations and estimates of the free energy. The multicanonical algorithm is implemented for non-Abelian gauge theories and is expected to be useful for studying the QCD deconfining phase transition. The paper concludes that the multicanonical algorithm provides a significant improvement over standard algorithms for first-order phase transitions, particularly for systems with strong first-order transitions.