2 rect detection experiments are the neutrino tele- scopes which are detecting the neutrino flux from DM captured and annihilated in the Sun or Earth. For example, Ref. [13] and Ref. [14, 15] give the neutrino constraints to the light elastic DM (eDM) and iSI DM which could account for DAMA results respectively. When the DM nucleus scattering is iSD, the constraints by the neutrino flux from the Sun can be dramatically different. The reason is that the kinetic energy requirement for a DM ( χ ) scattering inelastically with a nucleus ( N ) is For light elements like hydrogen, only very ener- getic DM particles can scatter with them and get captured in the Sun if δ is not very small. Then the overall capture rate with their dominant con- tributions from light elements in the Sun will be significantly reduced. The modified kinematics for inelastic scattering in Eq. (1) also largely reduced the kinetic phase space of DM captured in the Earth because of the small escape velocity of the Earth. Therefore, it is of importance to preform a detailed analysis regarding the above issues moti- vated by the recent DAMA, CDMS results. The paper is organized as follows. In Section II, we calculate the capture rate for both iSI and iSD DM in the Sun and we discuss the possible uncertainties in the calculation. In Section III, we obtain the constraint on the DM-nucleon inelas- tic cross section for different annihilation chan- nels from Super-Kamiokande (Super-K) and the expected event number from the on-going large volume neutrino telescope, IceCube. In Section IV, we will discuss the neutrino constraint from iDM captured in the Earth. Finally we conclude and discuss our studies in Section V. where µ ≡ m$_{χ}$m$_{N}$/ ( m$_{χ}$ + m$_{N}$ ) is the DM-nucleus reduced mass, δ is the mass split between two DM states. The escape velocity v ( r ) is approximated as [19] where M$_{⊙}$ is the mass of the Sun and v$_{c}$ = 1354 km/s and v$_{s}$ = 795 km/s. M ( r ) is the mass pro- file of the Sun which can be obtained by the Sun density profile [20] In the DM-nucleus center of mass frame, it is easy to see that in order to have a DM-nucleus inelastic scattering, the following condition is required C$_{A}$ = 〈 σv 〉 /V$_{⊙}$$_{eff}$ , C$_{E}$ is the inverse time for DM to escape via evaporation which will be neglected below since our DM is not very light. For typical DM we have considered, the time scale required to reach equilibrium between capture and annihi- lation, t$_{eq}$ = 1 / √ C$_{⊙}$C$_{A}$ , is much smaller than the age of the solar system so the annihilation rate is saturated at half of the capture rate Γ$_{A}$ = C$_{⊙}$/ 2. Therefore, calculating the DM capture rate in the Sun is crucial to estimate the final neutrino flux from the Sun [14–18]. Suppose a DM particle has a velocity u very far away from the Sun, at some point the escape ve- locity in a shell is v ( r ), the DM velocity w will be E$_{χ}$ > δ ( 1 + m$_{χ}$ m$_{N}$ ) . (1) w 2 = u 2 + v ( r ) $^{2}$. (3) µw 2 2 > δ, (4) v $^{2}$( r ) = v 2 c − M ( r ) M$_{⊙}$ ( v 2 c − v 2 $_{s}$) , (5) ρ ( r ) = ρ$_{0}$ exp( − B r R$_{⊙}$ ) , (6) C$_{⊙}$ = ∫ 4 πr $^{2}$dr ∫ du f ( u ) u w Ω( w ) , (7) f ( x ) dx = ρ$_{χ}$ m$_{χ}$ 4 √$_{π}$ x $^{2}$e − x $^{2}$e − η 2 sinh(2 xη ) 2 xη dx (8) ˙ N = C$_{⊙}$ − C$_{A}$N 2 − C$_{E}$N, (2) II. CAPTURE RATE FOR INELASTIC DARK MATTER IN THE SUN where f ( u ) is the DM velocity distribution at in- finity, Ω( w ) is the rate per unit time that a DM with velocity w scatter to a velocity less than v . We assume the DM velocity distribution far from the Sun follows a Maxwell-Boltzmann distribution in the Sun rest frame When DM particles travel through the Sun sys- tem, they may get trapped by the gravitational potential and continue to lose energy with every collision against nucleus and captured in the Sun. The time evolution of the DM population in the Sun is given by the differential equation where C$_{⊙}$ is the capture rate of the DMs in the Sun and annihilation rate is Γ$_{A}$ = C$_{A}$N $^{2}$/ 2 with where ρ$_{0}$ = 236 . 93 g/cm 3 and B = 10 . 098. The DM capture rate in the Sun is given by