Some embodiments of a medical device anchor system include an anchor device that secures a medical instrument (such as a catheter or the like) in place relative to a skin penetration point using subcutaneous anchors. In some implementations, the anchor device can be installed using a technique in which the subcutaneous anchors undergo relatively little or no flexing when being inserted through the skin into the subcutaneous region between the skin and underlying muscle tissue which may be occupied by fatty tissue.