  The gravitational field of both local and global non static cosmic strings in
the context of Lyra geometry are investigated. Local strings are characterized
by having an energy momentum tensor whose only non null components are $T_{tt}
= T_{zz}$ . As linearized Einstein equations are formally analogous to the
Maxwell equations, the exterior solution does not depend on the radial
distribution of the source and hence a Dirac d function was used to approximate
the radial distribution of the energy momentum tensor for a local cosmic string
along the z-axis: $T_{ab} = \delta(x) \delta(y)diag (\sigma, 0, 0, \sigma) $,
$\sigma $being the energy density of the string [A.Vilenkin.
Phys.Rep.(1985)121,263]. For a global string, the energy momentum tensor
components are calculated from the action density for a complex scalar field y
along with a Maxican hat potential. The gravitational field of the global
string is shown to be attractive in nature.
