The present study focuses on the numerical investigation of the Cauchy Magnetohyrodynamic (MHD) duct flow in the presence of an externally appliedoblique magnetic field, with a slipping and variably conducting wall portion ofthe duct walls. The underspecified and overspecified boundary informationsfor the velocity of the fluid and the induced magnetic field on both slippingand variably conducting duct wall and its opposite part, respectively, constitutes the Cauchy MHD duct flow problem. This study aims to recompute thevelocity of the fluid and induced magnetic field with specified slip length andconductivity constant, respectively, on the underspecified wall which is bothslipping and variably conducting. The governing coupled convection-diffusiontype MHD equations for the direct and inverse formulations are solved in onestroke using the dual reciprocity boundary element method (DRBEM). Boththe velocity and induced magnetic field and their normal derivatives to be usedas overspecified boundary conditions for the construction of Cauchy problemare obtained through the direct formulation of the problem. The well-posediterations are used in the regularization of the ill-conditioned systems of linear algebraic equations resulting from the DRBEM discretization of Cauchyproblem (inverse problem). Numerical solutions for the slip velocity and induced magnetic field are obtained for Hartmann number values M=5, 10, 50.The main advantages of the DRBEM are its boundary only nature and thecapability of providing both the unknowns and their normal derivatives onthe underspecified walls so that the conductivity constant and the slip lengthbetween them can be recovered at a low computational expense.