There is so much misinformation in the answers in this thread that I don’t know where to start. I just spent 4 points in reputation voting down the answers with misleading and wrong information in them.
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the Jet database engine (which is all that’s involved here, as the OP clarified with an edit) is by default multi-user — it was built from the ground up to be that way.
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sharing a Jet data store is very reliable when the network is not substandard. This means not a WAN and not wireless, because the bandwidth has to be sufficient for Jet to maintain the LDB file (for multi-user locking), which means a ping by your local PC’s instance of the Jet database engine once per second (with default settings), and because Jet can’t recover from a dropped connection (which is quite common in a wireless environment).
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the situation where Access falls down is when a front-end Access application MDB is shared (which is not the case for this poster). The reason it fails is because you’re sharing things that can’t be reliably shared and have no reason to be shared. Because of the way Access objects are stored in an MDB file (the entire Access project is stored in a single BLOB field in one record in one of the system tables), it’s very prone to corruption if multiple users open it. In my estimation, sharing an Access front end (or an unsplit MDB with the tables and forms/reports/etc. all in one MDB) is the source for 99.99% of corruptions of Access/Jet files.
My basic answer to the OP’s question is that, yes, Jet would be a great data store for an app of that size. However, if there’s any possibility at all for the user population to grow above 25, then it might be better to start off from scratch with a database engine that is more robust at higher user populations.