A longitudinal tear of the meniscus follows the curvature of the crescentic shock absorber that comprises the meniscus.

Significant longitudinal tear of the meniscus - running along in the same direction as the main fibre bundles.

To show how the tear would show up on a single MRI 'slice' through the tear (red line).
Healing of a longitudinal tear of the meniscus
Longitudinal tears are easier to repair than radial tears. They hold sutures well. If the tear is close to the outer rim where blood supply is good, a tear may often heal by itself.
Synonyms:
Circumferential tear
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CLINICAL PUBLICATIONS
The knee meniscus: management of traumatic tears and degenerative lesions. Beaufils P, Becker, R, Kopf S, Matthieu O and Pujol N. EFORT Open Rev. 2017 May; 2(5): 195–203.
Meniscal Preservation is Important for the Knee Joint. Patil SS, Shekhar A and Tapasvi SR. Indian J Orthop. 2017 Sep-Oct; 51(5): 576–587.