Medicaid Financing Reform Amendments of 1981 - Amends title XIX (Medicaid) of the Social Security Act to require a State plan to provide that, if the plan limits or restricts the choice of qualified providers from whom items or services may be obtained such restrictions and limitations: (1) may apply only to institutional providers and to the provision of laboratory services and medical devices; (2) must be pursuant to cost-effective arrangements; (3) must assure individuals reasonable access to services; and (4) may not provide for payment, with respect to inpatient hospital services, that (a) is less than the cost which is necessary for the efficient and economical delivery of services, or (b) results in a substantial adverse effect or access to at least one hospital with graduate medical education programs (if one is in the area).

Requires any laboratory services paid for under Medicaid to be provided for by a laboratory meeting standards set forth under the Medicare program (title XVIII of the Act).

Permits the use of the Medicaid prospective reimbursement system for inpatient hospital services furnished under the Medicare program if the hospital is reimbursed for Medicaid services utilizing such system.

Directs the Secretary of Health and Human Services to waive Medicaid program requirements if a State demonstrates that the waivers can reasonably be expected to improve administration, eliminate unnecessary regulatory burdens, or increase cost effectiveness. Prohibits any such waiver: (1) if the Secretary finds it would seriously impair substantial program goals; or (2) of certain requirements relating to eligibility, protection of life or safety, fair administrative process, or prevention of fraud or abuse.