Model numbers and serial numbers for washing machines are almost always behind the door or on the control panel although sometimes the number written on the control panel or dispenser drawer isn’t a model number but a model range ( Some washing machine manufacturers put a model number on the front of the machine which is useless ).
Some built in washing machines like to hide their model numbers. The one featured below shows an Ariston machine with a control panel that has nothing printed on it and the owner couldn’t find the model number so presumably it wasn’t behind the door.
On built in appliances the model and serial number are sometimes only shown behind the plastic kickstrip at the base of the machine. It’s worth checking behind the pump filter door if one is fitted as there could be a rating plate sticker there. If there is no serial number to be found anywhere the only option would be to get the appliance out, which can be a pain and you risk damaging flooring.