You might need to check whether your modem is supported, but you can setup an SMS gateway on a Linux PC using the Open Source SMS Server Tools 3.
I used to have two Wavecom GSM modems connected to a Linux server for sending appointment reminders for a large UK veterinary group.
http://smstools3.kekekasvi.com/index.php?p
The SMS Server Tools 3 is a SMS Gateway software which can send and receive short messages through GSM modems and mobile phones.
You can send short messages by simply storing text files into a special spool directory. The program monitors this directory and sends new files automatically. It also stores received short messages into another directory as text files. Binary messages (including Unicode text) are also supported, for example ring tone messages. It's also possible to send a WAP Push message to the WAP / MMS capable mobile phone.
The program can be run as a SMS daemon which can be started automatically when the operating system starts. High availability can be ensured by using multiple GSM devices (currently up to 64, this limit is easily changeable).
The SMS Server Tools runs on Microsoft Windows (with CygWin) and any Unix including Solaris, BSD, FreeBSD and GNU/Linux. This software needs a GSM modem (or mobile phone) with SMS command set according to the european specifications GSM 07.05 (=ETSI TS 300 585) and GSM 03.38 (=ETSI TS 100 900). AT command set is supported. Devices can be connected with serial port, infrared, USB or network modems using a socket.
2For SMS, you dont need a modem to do this. Assuming you have internet on the computer you can send SMS via email. The carrier address formats are readily available on google. For example ATT [10-digit phone number]@txt.att.net – P.Brian.Mackey – 2011-05-26T16:53:54.673
Thanks for that comment, but not all carriers accept number@carrier.gateway.com email messages. I still would like to have a way to use GSM network directly (i.e. without accessing Internaet gateways of any kind). I know that I can use Skype or SIP to send SMS from PC, but their SMS plans are more expensive as opposed to ones that cell carriers propose. – xyzman – 2011-05-29T18:06:58.273
I know you said you don't want to use an internet gateway solution, but there are plenty of free and low cost SMS gateways. – RobotHumans – 2011-06-27T16:30:58.940