I would be very, very careful about doing something like this and speak with an attorney about your options.
First, the practical issue: if you are on OPT now, you have less than one year left. Assuming your business does well (and I hope it would), what is your plan once the OPT runs out from a visa/immigration perspective? How would you remain here to run the business?
Now, the legal issues:
Starting your own company on OPT is highly questionable. While OPT is not employer-specific and is for "open-market" employment, it is intended for temporary employment for training purposes in your field - not entrepreneurship or self-employment. Even though you would be doing something in your field of study, it's hard to see how you would be receiving "training" if working for yourself rather than under the direction of more experienced individuals in that field.
Travel would be an even bigger problem: the requirements of the F-1/OPT are that you maintain "nonimmigrant intent" - the intent to remain in the U.S. only temporarily and return home at the end of your stay. Starting a business here is a pretty strong indication of an intent to remain on a longer-term basis.
There are visas which are more appropriate for beginning a business in the U.S., and if you qualify you would not have the same issues with traveling. So, speak to an attorney to determine if you might be eligible for something more in tune with what you hope to accomplish.
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If you want to know whether your proposed self-employment on OPT work authorization is viable, you should discuss it with the international student advisor at your school, and the department chair. OPT is work authorization tied to your student status, and the school is in the best position to advise you on whether you are in compliance with that status (plus it is a cost-effective resource since you are already paying/or paid a lot in tuition).
If you ask me, then I would say it is not allowed. And probably if you went down to your local office of USCIS, they would say the same thing; but perhaps you and your school will have a different view. The reason I would say it is not allowed is that it is too squishy. Everyone will say they are self-employed rather than unemployed and do whatever they want. Further, the point of practical training is to be trained. If you are self-employed, who is training you?
I am self-employed, so of course I don't knock self-employment. I am just trying to provide some realistic analysis of how this could be viewed.
You can travel abroad and re-enter on OPT if your passport is valid, your travel visa is valid, and you have a "job offer". It is definitely a gray area whether self-employment is a "job offer". You can review NAFSA guidance on this issue here: http://www.nafsa.org/_/Document/_/practice_advisory_2005-a.pdf.
NAFSA is the organization of international student advisors.Ask a similar question