  The asymptotic derivation of a new family of one-dimensional, weakly
nonlinear and weakly dispersive equations that model the flow of an ideal fluid
in an elastic vessel is presented. Dissipative effects due to the viscous
nature of the fluid are also taken into account. The new models validate by
asymptotic reasoning other non-dispersive systems of equations that are
commonly used, and improve other nonlinear and dispersive mathematical models
derived to describe the blood flow in elastic vessels. The new systems are
studied analytically in terms of their basic characteristic properties such as
the linear dispersion characteristics, symmetries, conservation laws and
solitary waves. Unidirectional model equations are also derived and analysed in
the case of vessels of constant radius. The capacity of the models to be used
in practical problems is being demonstrated by employing a particular system
with favourable properties to study the blood flow in a large artery. Two
different cases are considered: A vessel with constant radius and a tapered
vessel. Significant changes in the flow can be observed in the case of the
tapered vessel.
