Answer: Yes, squash can be grown on a trellis, but make sure the trellis is very sturdy. I like to use metal poles (like the ones you see along roadways as marker stakes) with hardware cloth (a heavier wire that has about 4-inch squares). Chicken wire is too "bendable." You're right that the vines can snap, but squash usually recovers and continues to grow. Training the vines up the trellis from the beginning alleviates that problem.
Smaller, lighter squash (summer, zucchini) are usually self supporting on the vine when trellised (especially if you pick them often and do not let them get too big and old).
For heavier squash, provide plenty of support or it will tear the vine off of the trellis. Gardeners have
fashioned all types of supports from sections of hosiery for smaller fruit on up to slings made of torn sheets or netting. Tie the support to the trellis when the fruit is the size of a baseball or softball and as the fruit grows it will provide adequate support. It is best to use materials that do not stretch too much or the growing fruit will cause the support too sag and not do its job. Check the supports periodically to make sure they are working right.
You may find this article, "Trellising Vine Crops",
http://www.garden.org/qanda/nga/articledetails.taf?id=642&kw... helpful. Thanks for writing!
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