Severance pay is a payment package offered to employees based on certain length of service and salary requirements.
According to the IRS, severance pay must be processed as income amounts to the employee as severance pay, and any payment for the cancellation of their employment contract (page 4 of Publication 525).
The IRS treats severance pay as supplemental wages because it is not a payment for services in the current pay period, but payment upon or after termination of employment.
Aggregate method — Severance pay is included and taxed as regular pay for the same pay period on the same check, or on a separate check.
Flat rate method — employer disregards the withholding allowances claimed or additional withholding amount requested by the employee on Form W-4, and uses a flat percentage rate (currently 25%) in calculating the amount of federal income tax.
If the employee is exempt from federal income tax on the W-4, the employer should not withhold anything.