In this paper we propose machine learning algorithms to estimate the sunshine duration at any region in Saudi Arabia using easily obtained parameters that include: maximum possible day length (So), extraterrestrial solar radiation at that particular location (Ho), latitude, longitude, altitude, and month number. Two neural network algorithms, namely, Particle Swarm Optimization (PSO) algorithm and Support Vector Machine (SVM), are used to estimate the sunshine duration (S). Due to the limited number of measurement stations, we use the leave-one-out strategy, where data from 40 measurement stations are used to build the model and data from the remaining 41st station are utilized to assess accuracy of the modeled system. This process is repeated for each of the 41 stations. Minimum mean absolute percent errors (MAPE) of 2.3% and 2.7% were obtained at Al-Madina station using PSO and SVM methods while the respective maximum values of 22.9% and 16.7% were observed at Al-Numas station. In general, higher MAPE values were found during summer time (June-August) and lower in winter time (January-February and November-December). Results indicate the viability of the proposed methods for estimating sunshine duration in Saudi Arabia, and the system is expected to perform similarly in other countries with similar environment.