To Study river systems different element of eco-system including hydrology, hydraulic, erosion processes sedimentation and river geometry should be taken under consideration. There is a time delay between changes taken place at independent variables and response of dependent variables, that by values and changes ranges and varability of ability is controlled. This research, for review geometric and hydraulic specifications of river, Firooze - shahjoob river in province North Khorasan was chosen. After analyze out put results of hydraulic model HEC-RAS, for discharge with return period 10 year for 37 reach during the river was action .The best equation from among regression relationships that including minimum standard error, minimum probability value and maximum coefficient of determination is selected. Result of research showed that power equations as more appropriate equation for relationships geometry-channel for river under study, that including minimum standard error, maximum coefficient of determination and p-value less than 0.1 than other models.The river systems study of different aspects of the natural environment includes hydrology, hydraulic, erosion processes sedimentation and river geometry, there is always a time delay between changes in the independent variables and response of dependent variables, that is controlled by values and changes ranges in the independent variables and also flexibility in depended variables. In this study, after analyzing the result of HEC-RAS hydraulic model for 10 years discharge in 37 reaches, the geometric and hydraulic characteristics of cross sections of Firooze - Shahjoob River in the province of North Khorasan were studied. The best equation was chosen among all of the regression equations that have the lowest standard deviation and p-value, and also has the highest coefficient of determination. The results showed that the exponential equation was the most appropriate equation for presenting the geometry channel relations of the studied river which had a standard error of 0.010, coefficient of determination of 0.88 and p-value 0.002 compared to other models.