This study sought to find out whether there is any significant relationship between the in trading volume shares of Syrian companies listed in the Damascus market Securities Exchange, and Volatility of stock returns monthly in that market, during the period 1-1- 2010 till 31-8-2014, and to discover what kind of that relationship (positive or negative correlation) in order to give appropriate weight to them for interpreting fluctuations in the volume of trading in the stock Damascus market Securities Exchange, or for predicting. When using the method of Nonlinear regression analysis method GARCH(1,1) to process the data related to Return on the stock in DSE we found that the relationship between the trading volume shares and volatility of stock returns wasn't statistically significant. This volatility in stock returns mustn't be taken into account as an important factor when trying to explain the reasons for fluctuations in trading volume market or when predicting.