The current thesis aims to study the characteristics of the A- type hydraulic jump at a positive step. The current research is divided into three parts. The first part aims to present a model that accurately evaluate the conjugate flow depth of the A-type hydraulic jump at a positive step. A relation is given to estimate the small rise of the flow at the step. Assuming the flow at the step as a concave curvilinear flow, a non-linear pressure distribution is considered. Applying one-dimensional momentum equation in the flow direction, an expression for the conjugate flow depth in terms of initial Froud number and step height is presented. In the second part, two approaches are presented to evaluate the length of the A-type jump. In the first approach, the end of the A-type hydraulic jump is assumed to be at a short distance downstream of the step brink and the hydraulic jump is modeled as a turbulent wall-jet. Knowing that the pressure gradient is the only difference between the hydraulic jump and the wall-jet, pressure gradient is taken into account as an effective parameter. Using dimensional analysis, an expression for the maximum velocity of the wall-jet is extracted. Applying appropriate expressions for the velocity distribution and the growth rate of the jump, the jump length is expressed in terms of the initial Froud number. In the second approach, the end of the jump is assumed to locate at the step brink and the jump length is calculated by the revised Beirami-Chamani relation for the justify; MARGIN: 0in 0in 0pt; unicode-bidi: embed; DIRECTION: ltr; mso-layout-grid-align: none" The results confirm the efficiency of the theory of curvilinear flow to estimate the conjugate flow depth. The accuracy of the predictions decreases as the Froud number increases and the relative step height decreses. The conjugate flow depth increases with initial Froud number with an approximate linear trend and with a slope of almost unity. It is concluded that predictions of the jump length by the first approach are always higher than experimental data and this approach is is not applicable at low Froud numbers. The second approach estimates the jump length accurately, in which the jump length increases sharply with initial Froud number and then decreases mildly. Despite common belief, existence of a positive step against has no considerable effect on the energy dissipation rate of the jump. Key Words Hydraulic jump, Positive step, Conjugate flow depth, Curvilinear flow, Jump length, turbulent wall-jet, Pressure gradient, Energy dissipation.