  We analyze several mechanisms leading to errors in a course of measurement of
a superconducting flux-biased phase qubit. Insufficiently long measurement
pulse may lead to nonadiabatic transitions between qubit states $|1>$ and
$|0>$, before tunneling through a reduced barrier is supposed to distinguish
the qubit states. Finite (though large) ratio of tunneling rates for these
states leads to incomplete discrimination between $|1>$ and $|0>$.
Insufficiently fast energy relaxation after the tunneling of state $|1>$ may
cause the repopulation of the quantum well in which only the state $|0>$ is
supposed to remain. We analyze these types of measurement errors using
analytical approaches as well as numerical solution of the time-dependent
Schr\"{o}dinger equation.
