There are several providers in Ukraine which allow people to send free SMS to their subscribers through their web sites.

Here a list of such sites sorted by provider.
(these numbers are the ones which comes after +38)

Kyivstar

http://www.kyivstar.ua/en/sms
Free
work only with numbers that start with: 067, 098, 097, 096, 039, 063, 093, 068
max 100 sms/day

MTS (ex. UMC, Jeans)

http://www.mts.com.ua/eng/sendsms.php
Free
work only with numbers that start with: 050, 066, 095, 099

Beeline

http://beesms.beeline.ua
Require registration.
work only with numbers that start with: 068, 039, 063, 093, 067, 096, 097, 098

Life:)

http://www.life.com.ua/index.php?area=lifebox&lng=en&page=15-27
NEW! free.
You can send a max of 3 SMS and MMS / day.
Works with: 063 and 093.