High blood pressure is not a joke diagnosis. There was one study (BBC link) that suggested that acupuncture used with electrical stimulation had some effect on rats. Notice that traditional acupuncture had no effect, so any moxibustion or cupping treatment would likely be as useless. Before you begin investigating unproven modalities you ought to familiarize yourself with www.quackwatch.org, particularly the "Questionable Products, Services, and Theories" section.
I have to respectfully disagree with the above. Acupuncture is a very powerful treatment and I have seen it work for very severe health problems, most notably for nerve damage in connection with my wife. To call acupuncture quackary is narrow minded and incorrect.
After watching the success with my wife, I had opportunity to witness for myself a "blind study" that proved how powerful acupuncture is: One day, quite unexpectadly, our beloved dog was about to walk outside when her legs just gave out. She lost the use of her hind legs. As it turns out she had a severe case of hip displaysia that is considered incurable without surgical intervention. We were having to carry our poor girl out to go to the bathroom every time she needed to go. We were considering euthanasia, but learned of an animal accupuncturist who was having success with horses and came highly recommended. We decided that we would give it a try, but were prepared to take care of matters if the acupuncture had no effect.
With the very first treatment our Border Collie was able to walk, although very wobbly. After a week of treatments she was able to walk again, although she will always have a little bit of a sway when she walks. We have to take her in periodically for treatment when her gait gets wobbly, however it sure beats the alternative. Just for the record, when our dog went down we initially treated her conventionally for a week, prior to finding the acupuncturist, with no success. She did not gain use of her legs until she recieved acupuncture. If you can call that quackary, then my dog is quacking like a duck as she is walking around today.
To answer the original question, I have heard that acupuncture is quite effective for high blood pressure, however it is important to find the right acupuncturist. Like any field, including the medical field, there are good practitioners and bad practitioners. If you choose to use acupuncture be sure to do research, ask questions, and talk to people that get treated with acupuncture. Many times there can be many acupuncturists to choose from, but there will be one acupuncturist in the community that has most of the patients because he, or she, is skilled. I know that is the case in my community. Good luck with whatever health choice you make.
exjdub