This paper presents a 3D finite element upper arm model, validated by experiments as well as clinical data, used to study the error introduced in blood pressure measurements due to variability of arm tissue mechanical properties. The model consists of three separate cylindrical parts: soft tissue, bone and brachial artery. The artery volume changes under the cuff are used to represent the cuff pressure oscillations for analyzing blood pressure measurements. These oscillation trends are identical to observed clinical data. Also an upper arm simulator is designed and built for model validation. The model shows that the variation of soft tissue compressibility introduces an error up to 5% in blood pressure measurements. It is also revealed that the variation of the brachial artery and arm tissue stiffness has an insignificant effect on oscillometric blood pressure measurement method.