  Let $X$ be a complex projective variety, and let $E_{\ast}$ be a parabolic
vector bundle on $X$. We introduce the notion of \textit{parabolic Seshadri
constants} of $E_{\ast}$. It is shown that these constants are analogous to the
classical Seshadri constants of vector bundles, in particular, they have
parallel definitions and properties. We prove a Seshadri criterion for
parabolic ampleness of $E_{\ast}$ in terms of parabolic Seshadri constants. We
also compute parabolic Seshadri constants for symmetric powers and tensor
products of parabolic vector bundles.
