Assuming you are using bitcoin core, theoretically, you only need to copy "wallet.dat" to another computer and you can access the same set of addresses. I am not sure whether both wallets will create the same address when you create a new address in both wallets. Better not do this way, or only create new addresses on one wallet and copy to the other.
As long as the hidden pool of addresses (100 by default) is not used they create the same addresses even for change. Afterwards however the addresses will be different. So over time the 3 instances of the same wallet.dat will change and no longer be in sync. HD wallets (armory, electrum, multibit HD) are better for this.