Plastic until it dies.

Even plastic is not entirely effective - equisetum have complicated and very far reaching root systems. They will find where the plastic is not and pop up - they will also weasel in between the seams to emerge. There is no groundcover that will adequately supress them - they've been around since the dinosaurs and plant species with that type of longevity are extremely well adapted at survival.

Your only hope at control is to pick off the top growth as soon as it emerges. Eventually the lack of ability to photosynthesize will weaken the plants to the point where they will no longer be a nuisance. Unfortunately, even broad spectrum herbicides have little effect on these pests.

FWIW, horsetails are one of the most difficult weeds to control let alone eradicate. You have my sympathies.

Thanks GardenGal48, I have been snipping the growth above the soil with scissors and weedwackers, this year. Last year I tried to pull off the roots, I have done more damage than good. This nasty weed seems to cluster around shrub and perennial roots. I am wondering it is not somekind of parasite. Removing these around the strawberries and ajugas are a nightmare. I may have to wack the stawberries as a last resort. In shade however, these are sparse and taller. In sun, they are spready like crazy especially after rains.
What a waste of time. Thanks for your sympathies.
-lg