A tearaway sheath assembly (100) having a splittable sheath tube (102) a splittable hub (110), a split valve (150,250) and a split cap (180). The valve (150,250) has a slit (158,258) at least partially across the transverse distal section (154) such that transverse distal section may be displaced laterally during insertion through the slit (158,258), of a dilator (200) or a catheter. The valve (150,250) is formed in two separate halves (152A,152B;252) that are fused or adhered to each other to form a sealed weak bond (154) that is easily broken during splitting of the sheath; each valve half is mechanically affixed in a proximal valve-receiving recess (130) of the hub such as by anchor posts (136) extending through apertures (166A,166B) in ears (164A,164B) of each valve half. A two-part cap (180) is affixed to the hub proximal end (120) and traps the valve between itself and the hub. Pairs of opposed gaps (184,122) of the cap (180) and the hub (110) are aligned with lines of weakness or seams (106) of the sheath tube (102) and the weak bond (154) of the valve, facilitating splitting of the assembly (100) when desired by the practitioner to peel it away from the inserted catheter.