  We investigate a Bianchi type-I (BTI) cosmology with k essence and find the
set of models which dissipate the initial anisotropy. There are cosmological
models with extended tachyon fields and k essence having constant bariotropic
index. We obtain the conditions leading to a regular bounce of the average
geometry and the residual anisotropy on the bounce. For constant potential, we
develop purely kinetic k-essence models which are dust dominated in their early
stages, dissipate the initial anisotropy and end in a stable de Sitter
accelerated expansion scenario. We show that linear k field and polynomial
kinetic function models evolve asymptotically to Friedmann-Robertson-Walker
(FRW) cosmologies. The linear case is compatible with an asymptotic potential
interpolating between $V_l\propto \phi^{-\gamma_l}$, in the shear dominated
regime, and $V_l\propto\phi^{-2}$ at late time. In the polynomial case, the
general solution contains cosmological models with an oscillatory average
geometry. For linear k essence, we find the general solution in the BTI
cosmology when the k field is driven by an inverse square potential. This model
shares the same geometry than a quintessence field driven by an exponential
potential.
