"Mainframe" is the class of computers that were initially developed in the 1960s. IBM System/360, which later became S/370, S/390, XA, ESA and now z/series is one of the most important. A mainframe *can* act as a server, but so can almost any other computer, so "server" is definitely not the correct translation. "server" is about a specific way of using a computer, not the class of computer. I've worked with mainframe computers as a systems programmer from 1984 to 2003, out of which 12 years with IBM. The last two years were in France, where mainframe is also called "grand systèmes". A simple google search will reveal countless hits. Mainframe computers are not out of date, but their use is limited to computing centres that need intensive treatment of large quantities of date: Airlines/train reservation centres, banks, insurance companies and other companies with large quantities of customers. You would be unable to buy a single train ticket in France without mainframes.

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Note added at 4 hrs 18 mins (2005-03-14 14:07:54 GMT)
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As for anglicism or not, any French professional will understand mainframe and grands systèmes equally well. The documentation is probably in English anyway. However, translating words to French causes fewer problems than translating acronyms like ISDN to RNIS, which effectively works as an obstacle to comprehension. Fortunately, that seems to be a thing of the past, as recent acronyms like ADSL shows.

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Note added at 5 hrs 9 mins (2005-03-14 14:59:30 GMT)
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More resources:

http://www.mainframes.com/whatis.htm - a detailed article looking at the various aspects of a mainframe.

http://www.sdsusa.com/dictionary/glossAZ/m.htm and
http://www.sdsusa.com/dictionary/ :
\"Mainframe: Mainframes used to be defined by their size, and they can still fill a room, cost millions, and support thousands of users. But now a mainframe can also run on a laptop and support two users. So today\'s mainframes are best defined by their operating systems: Unix and Linux, and IBM\'s z/OS, OS/390, MVS, VM, and VSE. Mainframes combine four important features: 1) Reliable single-thread performance, which is essential for reasonable operations against a database. 2) Maximum I/O connectivity, which means mainframes excel at providing for huge disk farms. 3) Maximum I/O bandwidth, so connections between drives and processors have few choke-points. 4) Reliability--mainframes often allow for \"graceful degradation\" and service while the system is running.\"

http://www.hwcs.com/news_events/glossary.asp: \"mainframe - a very large computer that is able to support thousands of users at the same time. Users access the mainframe through a terminal.\"

http://dictionary.reference.com/search?q=mainframe: Several definitions.

None of them indicates that \"server\" should be an equivalent, but the mainframe concept is not set in stone either. IBM themselves avoid to define \"mainframe\" in their computing glossary online.

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Note added at 6 hrs 54 mins (2005-03-14 16:43:54 GMT)
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Comment to Joelle: If most servers are mainframes or not is besides the point. \"server\" is one particular way of using a mainframe, and web hosting is only a recent way of using a mainframe. When mainframes were invented in the 1960s, there was no web, and the client-server concept had not yet been invented.

If you look at road traffic, you might say that most vehicles are cars, and the only vehicle you have ever driven is a car, so car=vehicle. But you know that is not the case, because there are lorries, buses, motor bikes etc.

Mainframes can be used for all sorts of computing: development, programming, testing, database, time-sharing, interactive use, batch, network hub, word processing, document sharing, hosting other operating systems..., so why do you want to reduce it to \"server\"? It may happen to be its only purpose where you are working, but the reality is more complex.