Mixed u-p finite element formulations represent a popular technique in the solution of near-incompressible and incompressible problems [1]. We present a procedure based on the scaled boundary finite element method [2] to construct stable u-p elements. In this procedure, the shape functions of an element are built from the solution of a Poisson equation defined on the element domain. The nonhomogeneous term of the Poisson equation is expressed as a polynomial [3]. The boundary of the element domain is discretized using finite element formulations and a scaling centre is selected inside the domain. The solution within the domain is expressed analytically in the radial direction emanating from the scaling centre and numerically along the directions parallel to the boundary, leading to a system of nonhomogeneous ordinary differential equations (ODEs). A new solution technique of the ODEs is proposed by transforming the system of nonhomogeneous equations into a system of homogeneous equations. An efficient and concise algorithm to compute the shape functions is proposed This semi-analytical procedure provides insight into the selection of interpolations of the displacement (u) and pressure (p) fields of stable mixed elements. Numerical examples are presented for validation.