Hi Vera, my husband is a specialist in this area and here is his advice:
Most non-US persons would not have a US tax number. The form W8-BEN certifies your non-US tax status and may be requested by any financial institution globally. If you are providing the form to a non-US financial institution, neither the foreign TIN (tax identification number) or the US TIN is required. If you are providing to a US financial institution, the foreign TIN (non US Tin) and your date of birth) may be required.
In other words, because the form certifies your non-US tax status, a US tax identification number is not a required field. If however you are providing W8BEN to a US financial institution, you may be required to provide your foreign TIN and date of birth.
Hope that helps.