A tunnel boring machine for controlled boring of an elongated curvilinear tunnel in earthen strata. The tunnel boring machine comprises: cutting means for engaging the tunnel face and removing material therefrom to elongate the tunnel during a cutting strocke; elongated body means for supporting various machine components; elongate thrust arm means for urging the cutting means against the tunnel face during a cutting stroke and for advancing the elongated body means along the tunnel between cutting strokes, the thrust arm means being extendable and retractable from the body means along a thrust arm axis coaxial a machine longitudinal axis; forward lateral positioning means operably mounted on a forward portion of the body means for selectively controlling the lateral positioning of a forward portion of the body means within the tunnel; rear lateral positioning means operably mounted on a rear portion of the body means for selectively controlling the lateral positioning of the rear portion of the body means within the tunnel; forward transverse positioning means operably mounted on a forward portion of the body means for selectively controlling the transverse positioning of a forward portion of the body means within the tunnel; rear transverse positioning means operably mounted on a rear portion of the body means for selectively controlling the transverse positioning of the body means within the tunnel; whereby the machine longitudinal axis is selectively transversely and/or laterally positionable relative the longitudinal axis of the tunnel through the use of the forward and rear lateral positioning means and the forward and rear transverse positioning means; and tunnel gripping means operably mounted on the body means for selectively grippingly engaging the peripheral sidewall of the tunnel to prevent rearward movement of the body means during a cutting stroke. Various methods of operation of the machine are described.