Upper Body

I have been running on and off for about 5 years now and concentrate on 5k's and 10k's. My PB for a 10k is 41m12 (18m50 for a 5k) and I really want to get under 40mins. I have tried loads of different styles of training - short speedy runs and longer endurance based runs.

 I find that I manage to get the strength back into my legs and I get my lungs working fairly quickly after a few sessions BUT I do find that I always feel weak in the arms and the stomach. Whereas my legs are visually stronger through running my upper body doesnt seem to strengthen too much.

 I am not a big fan of gyms weights so I was wondering if there are any alternative methods to gain better core strength? 

 Thanks in advance!