Download a free equipment rental agreement template, and view sample lease and leasetoown agreements for construction equipment. An equipment lease agreement is a legal contract where the owner allows another party (lessee) to use equipment in exchange for payment.You can use this document to outline the terms and conditions of an equipment rental. This Equipment Rental Agreement ("Agreement") is effective as of the date of last signature ("Effective. The downloadable form is designed to institute a concrete arrangement, establishing the terms and conditions to be followed for the duration of the contract.