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