The phone itself should be able to send the same text message to every contact you select in the SMS app. However your carrier will very likely limit the number of messages that are actually sent. I've read reports on AF of things like a maximum of between 10 & 25, depending on your carrier. Which is probably to prevent spammers and abuse. There are bulk SMS services available online, but not free probably.
Large groups of people tend to use Facebook, or Whatsapp, or something, for group-wide messages, memos, chats, etc.