Step 1: Understanding magnetic field in a solenoid.
A solenoid is a long wire wound in a cylindrical shape, and when current flows through it, it produces a magnetic field. The magnetic field lines inside the solenoid are parallel and uniform, aligning in the same direction as the axis of the solenoid.
Step 2: Conclusion.
Thus, the direction of the magnetic field inside a current-carrying solenoid is parallel to its axis.
\[
\boxed{\text{parallel to axis}}
\]