An apparatus and method for rapid determination of erythrocyte sedimentation rates for a blood specimen (29) which can be linearly transposed to Westergren sedimentation rates. The method includes the steps of inducing accelerated rouleaux formation in the specimen (29) in an amount sufficient to begin settling at substantially the decantation rate for the specimen. In one embodiment a structure (27) which produces a very thin cross-sectional region (37) of the specimen (29) inside the lumen (23) of a specimen container (21) is provided to accelerate rouleaux formation. In an alternative embodiment (120), accelerated rouleaux formation is accomplished using a centrifuge (122). A third embodiment employs a movable rod (223) mounted inside the specimen tube (221) to induce accelerated rouleaux formation. All embodiments of the process next employ gravity settling the specimen in a near horizontal oriented container (21, 121, 221). Thereafter, the amount of settling occurring is determined. A sealed specimen container (21, 121, 221) which permits thorough mixing of blood in a very small diameter container for use in performing the method also is provided.