Adding max(value)+1 in new row, can this be a problem?

In a SQL Server table I have the following 2 columns:

RowId: primary key, numaric, identity column and auto insert.
MailId: Non key, numaric, non identity and non auto insert.

Mail Id can be duplicate. In case of new MailId I will check max(MailId)+1 and insert it in new row and in case of duplication value will be coming as parameter.

Logic looks fine but here is an issue, I was just considering (yet chacnes of accurance are ver low) In the same time there can be two different new MailId requests. Can this casue logical error ? For example when code checked max(MailId)+1 was 101 and I stored it in a variable but may be before next insert statment executs a new record inserted in table. Now max(MailId)+1 in table will be 102 but value in variable will be 101 ?

Any suggestion please I want to control this error chances as well.

EDIT

(I am not using identity(1,1) because I also have to pass custom values in it)

Solution

Why would you use a custom-rolled Identity field when there is such a great one already in SQL Server?

Just use INT Identity (1,1) for your ID field and it will automatically increment each time a row is inserted. It also handles concurrency much better than pretty much anything you could implement manually.

EDIT:

Sample of a manual ID value:

SET IDENTITY_INSERT MyTable ON

INSERT INTO MyTable (IdField, Col1, Col2, Col3,...)
VALUES
(1234, 'Col1', 'Col2', 'Col3',...)

SET IDENTITY_INSERT MyTable OFF

You need to include an explicit field list for the INSERT.