In this talk, we will introduce an arbitrarily high-order fully well-balanced numerical methods for the one-dimensional blood flow models that is based on a continuous approximation of the solution. The degrees of freedom are point values at cell interfaces and moments of the solution inside the cell. We first combine the conservative and primitive formulations of the studied hyperbolic system in a natural way. The point values and moments will then be evolved by two different forms of PDEs. We show how to deal with both the conservative and primitive forms of PDEs in a well-balanced manner. It is worth noting that we achieve well-balanced evolution for the primitive variables by directly employing the finite difference discretization method with an upwind flavor on the equilibrium variables. This renders the proposed scheme free from the need for nonlinear equation solvers. The developed schemes are capable of exactly preserving both of the one-dimensional equilibria. We demonstrate the behavior of the proposed new scheme on several challenging examples. Blood flow model, Well-balanced, Arbitrarily high-order, Steady state