Economic growth and development remains an important policy issue for most of the states in the world, which is a particular issue for late developing countries, as they have very much relied on 'state' for economic growth and development. As a result, the experience in the 20th century demonstrates a secular increase in the growth of government expenditures all over the world. Hence, the role of government expenditures in contributing to long run economic growth continues to be an important topic and the subject of much debate. Saudi Arabia economy is one of late developing countries. While its economy is characterised by an open and private economy, the government remains to have a large role in the economy through its expenditures financed largely by revenues generated from oil. While the Saudi economy has grown and developed, the government has also responded to the increased demand for social services such as education and healthcare in addition to other infrastructure investments for development purpose. Therefore, the process of economic growth and development has resulted in growth of government expenditures. This research, thus, aims at modelling of government expenditures and economic growth nexus in the case o Saudi Arabia for the period of 1968-2010 by testing a number of models developed in the literature: Wagner's Law, Keynesian Relations and Peacock and Wiseman's Displacement Effect. The analysis modelled within the time series econometric techniques including co-integration test, Granger causality test and the error correction model (ECM). The findings obtained from the analyses find that the Wagnerian proposition can explain the growth of government in Saudi Arabia, which holds for both the oil and non-oil income cases. The result indicates the existence of strong feedback causality for all the versions of Wagner's law in the long run. The findings also note that the three versions of Keynesian Relations found to be held for both general income and non-oil income in the case of Saudi Arabia. In addition, the findings also support for the Displacement Effect mainly due to international political developments and trends in oil prices, as such events resulted deviation from the linear growth in the government expenditures over the average growth and it is observed that government expenditure growth continued its gradual growth from the new level. This study, thus, concludes that growing economic activity of the state has marked the Saudi Arabian economy over the period in question. While this partly can be explained due to economic reasons such as the need for economic development and responding to the demands of a growing population, but also the rentier economy nature of the Saudi political economy necessitates increasing government expenditures for political stability.