  There are a number of reasons to study wormholes with generic cosmological
constant $\Lambda$. Recent observations indicate that present accelerating
expansion of the universe demands $\Lambda>0$. On the other hand, some extended
theories of gravitation such as supergravity and superstring theories posses
vacuum states with $\Lambda<0$. Even within the framework of general
relativity, a negative cosmological constant permits black holes with horizons
topologically different from the usual spherical ones. These solutions are
convertible to wormhole solutions by adding some exotic matter. In this paper,
the asymptotically flat wormhole solutions in a generic cosmological constant
background are studied. By constructing a specific class of shape functions,
mass function, energy density and pressure profiles which support such a
geometry are obtained. It is shown that for having such a geometry, the
wormhole throat $r_0$, the cosmological constant $\Lambda$ and the equation of
state parameter $\omega$ should satisfy two specific conditions. The
possibility of setting different values for the parameters of the model helps
us to find exact solutions for the metric functions, mass functions and
energy-momentum profiles. At last, the volume integral quantifier, which
provides useful information about the total amount of energy condition
violating matter is discussed briefly.
