The requirement for an Economic Operators Registration and Identification number (EORI) will depend on which party is the exporter of record (EOR) and the importer of record (IOR):
:: If you are sending goods across the customs border after Brexit, both the EOR (exporter of record) and the IOR (importer of record) will require an EORI number.
:: If you are clearing customs into or out of any EU member state, you will only need an EU EORI number.
:: If you are clearing customs into or out of the UK, you will only need a UK EORI number.
This means that UK or EU sellers sending shipments to both sides of the border will require both a UK and an EU EORI. One EU EORI number will be sufficient for all EU countries.
If you are fulfilling your own orders and only shipping goods directly to customers on the other side of the border, you may not need an EORI number. Contact your logistics agent or tax advisor for further details.
You can find more information on how to get a UK EORI here: https://www.gov.uk/eori
Information on how to request an EORI number for EU countries can be found here: https://ec.europa.eu/taxation_customs/business/customs-procedures/general-overview/economic-operators-registration-identification-number-eori_en