I do some mechanical work on bikes. I am always learning something.

When it comes to wheels I am very inexperienced.

My rear wheel has a wobble. The wobble is not back forth but up and down.

Is this due to the tension of the spokes? Or is my wheel damaged?

As I spin the wheel and flex the spokes I can tell some spokes have less tension than others.

Please help.

Could be a couple of things. If the rim is out of round, it is due to spoke tension being uneven. Take it to a shop and have the rim trued (ask around to find out who is good at truing rims in your area). Or, the rim could be round and the tire bead not seated evenly around the rim.