The paper investigates two-phase mixture flows in sloping pipes employing two computational methods in the transitional region of pipe slope angle. We used methods of computing two-mixture flows in horizontal and vertical pipes as the basis for our equations. When flowing downwards through a sloping pipe, the solid phase volume ratio distribution changes most significantly: an axisymmetric flow through a vertical pipe transforms into a flow featuring a markedly non-uniform distribution of the solid phase along the vertical plane in the sloping pipe. When flowing upwards, the solid phase volume ratio profile is inversely transformed. Comparison of the experimental and computational data showed that the datasets are in a sufficiently good agreement. The computational method developed is semi-empirical and may be recommended for calculating hydraulic gradient in sloping pipes.