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The present study deals with a spatially homogeneous and anisotropicBianchi-II cosmological models representing massive strings in normal gauge forLyra's manifold by applying the variation law for generalized Hubble'sparameter that yields a constant value of deceleration parameter. The variationlaw for Hubble's parameter generates two types of solutions for the averagescale factor, one is of power-law type and other is of the exponential form.Using these two forms, Einstein's modified field equations are solvedseparately that correspond to expanding singular and non-singular models of theuniverse respectively. The energy-momentum tensor for such string as formulatedby Letelier (1983) is used to construct massive string cosmological models forwhich we assume that the expansion ($\theta$) in the model is proportional tothe component $\sigma^{1}_{~1}$ of the shear tensor $\sigma^{j}_{i}$. Thiscondition leads to $A = (BC)^{m}$, where A, B and C are the metric coefficientsand m is proportionality constant. Our models are in accelerating phase whichis consistent to the recent observations. It has been found that thedisplacement vector $\beta$ behaves like cosmological term $\Lambda$ in thenormal gauge treatment and the solutions are consistent with recentobservations of SNe Ia. It has been found that massive strings dominate in thedecelerating universe whereas strings dominate in the accelerating universe.Some physical and geometric behaviour of these models are also discussed.

Bianchi Type-II String Cosmological Models in Normal Gauge for Lyra's Manifold with Constant Deceleration Parameter