In Sofia, Bulgaria there are two parking zones - blue and green, and for both of them is possible to pay via SMS. My problem is that I have no longer a Bulgarian SIM-card, and I wonder if it's possible to pay with a foreign SIM?
I don't think it's possible. The Center for City Mobility (Център за градска мобилност) in Sofia which is responsible for the rapid transit system in the city has this to say on SMS parking (emphasis mine):
Customers of Bulgaria’s mobile operators may park on public streets and squares in the municipality, which are within the limits of the Blue Zone Scheme for paid short-stay parking...
This doesn't mention specifically that non-Bulgarian operators are excluded, but from experience with similar systems in other countries, this won't be possible. I assume this is done to simplify collection of what is due without having to deal with every single mobile operator in the world.
You might also be interested in the SMS Parking application for Android, though you still need to have a SIM card from a Bulgarian mobile operator.