Tryndamere is a melee AD carry. He needs to get fed. Jungling allows Tryndamere to feed himself with minimal harassment from the enemy team. Considering both how squishy and how limited in his range Tryndamere is, this can make playing him early-game a whole lot more fun.

I do not recommend trying this out in a higher ELO setting. I have never tried it, so do so at your own peril.

I have formatted my runes based on my personal preferences. As with all rune configurations, how you decide to rune your Tryndamere will matter more to you and less to your outcome. Choose runes you're comfortable using.

Marks
are my choice. Attack speed helps with fury generation, which means more Bloodlust. These runes have maximum value at level 1, which helps with early jungling.
For better late game damage or different methods of generating fury, other options are:
greater mark of desolation
Seals
is your best bet as a jungler. I have rarely seen someone deviate from this seal setup. There are no alternatives; those runes are like nine tiny s.
Glyphs
is what I pick, but considering Undying Rage, you may consider those glyphs a less-than-stellar choice. However, glyphs give us poor decisions; if you're unhappy with the one's I've chosen, just grab or some other mirror of a mark choice.
Quintessences
gives you better chasing as well as more mobility between lanes. As with glyphs: if you're unhappy with the option that only quintessences really bring, just use something like .