Yes, it is possible to block a number on a landline. You need to go through your phone's manual for that as every landline is built slightly differently. If you have misplaced the manual then you can find it online. Make sure the manual is on your landline. You will probably get a dedicated section for blocking in the manual. Follow the written instructions to block the number. If you still don't find a way to block then you can contact your carrier. You will get options like anonymous call rejection or blocking a specific number. The carrier will help you with that and you may have to pay some extra money for it too. If all of these don't work and you only want to block specific numbers. Then you can try the priority ring feature. Many landlines have it, check if the one you have got has it too or not. This feature lets you change the ringing sound of the calls. So that you can easily distinguish between them and decide whether to accept or not.