In the past the long run objective of monetary policy was a balanced budget, but more recently it has focussed on price stability. Price level stabilization had many proponents during the 1920s and 1930s and continues to have advocates today. The central banks of the US, New Zealand, Germany, and others espoused it during the last two decades. Price level determination and hence stabilization are important issues for economies since they determine the expectations of policy makers and individuals. Price level stability implies a steady inflation rate; it is similar to zero inflation but it differs in that price level stability returns the price level to its initial level while zero inflation implies offsetting a rise in prices and aims to stop future price rises. Price level stability is the better objective for monetary policy since private individuals desire a stable and predictable monetary environment to engage in business transactions. Therefore, the price level will be more predictable under a stable price objective than under zero inflation one. This also brings long run price stability, because of a stable monetary policy. The paper covers several classical views of price level stability and stabilization: how price level is theoretically and historically determined and stabilized under free banking and central banking regimes, as well. Consequently, empirical evidence concerning the price level stability under free banking is mixed.